feat: Add precalculus course to catalog (#66089)

Co-authored-by: Huyen Nguyen <25715018+huyenltnguyen@users.noreply.github.com>
2026-05-28 18:26:54 +00:00 · 2026-03-12 10:55:17 -07:00
parent ab14a6a9b1
commit 4015c354b9
56 changed files with 1763 additions and 0 deletions
@@ -1076,6 +1076,60 @@
      }
    }
  },
+  "introduction-to-precalculus": {
+    "title": "Introduction to Precalculus",
+    "summary": [
+      "Learn the fundamentals of precalculus, including functions, and trigonometry."
+    ],
+    "intro": [
+      "Precalculus is a branch of mathematics that prepares you for calculus. It covers a wide range of topics including functions, and trigonometry."
+    ],
+    "note": "",
+    "blocks": {
+      "function-basics": {
+        "title": "Function Basics",
+        "intro": [
+          "In these videos, you will learn about functions and how to work with them."
+        ]
+      },
+      "angles-and-circular-motion": {
+        "title": "Angles and Circular Motion",
+        "intro": [
+          "In these videos, you will learn about angles and circular motion."
+        ]
+      },
+      "right-triangle-trigonometry": {
+        "title": "Right Triangle Trigonometry",
+        "intro": [
+          "In these videos, you will learn about right triangle trigonometry and how to work with it."
+        ]
+      },
+      "trig-graphs-inverses": {
+        "title": "Trigonometric Graphs and Inverses",
+        "intro": [
+          "In these videos, you will learn about trigonometric graphs and inverse functions."
+        ]
+      },
+      "solving-trig-equations": {
+        "title": "Solving Trigonometric Equations",
+        "intro": [
+          "In these videos, you will learn how to solve trigonometric equations."
+        ]
+      },
+      "trig-identities-formulas": {
+        "title": "Trigonometric Identities and Formulas",
+        "intro": [
+          "In these videos, you will learn about trigonometric identities and formulas."
+        ]
+      },
+      "advanced-trig-conics": {
+        "title": "Advanced Trigonometry and Conics",
+        "intro": [
+          "In these videos, you will learn about advanced trigonometry and conic sections."
+        ]
+      }
+    }
+  },
  "introduction-to-bash": {
    "title": "Introduction to Bash",
    "summary": [
@@ -1276,6 +1276,7 @@
      "foundational-c-sharp-with-microsoft-cert": "Foundational C# with Microsoft Certification",
      "learn-python-for-beginners": "Learn Python for Beginners",
      "introduction-to-algorithms-and-data-structures": "Introduction to Algorithms and Data Structures",
+      "introduction-to-precalculus": "Introduction to Precalculus",
      "learn-prompting-fundamentals": "Learn Prompting Fundamentals",
      "a2-english-for-developers": "A2 English for Developers",
      "a2-english-for-developers-cert": "A2 English for Developers Certification (Beta)",
@@ -1471,6 +1472,7 @@
        "information-security": "Information Security",
        "computer-fundamentals": "Computer Fundamentals",
        "computer-science": "Computer Science",
+        "math": "Math",
        "databases": "Databases",
        "bash": "Bash",
        "git": "Git",
@@ -82,6 +82,7 @@ const iconMap = {
  [SuperBlocks.CssAnimations]: Code,
  [SuperBlocks.LearnPythonForBeginners]: PythonIcon,
  [SuperBlocks.IntroductionToAlgorithmsAndDataStructures]: Code,
+  [SuperBlocks.IntroductionToPrecalculus]: CollegeAlgebra,
  [SuperBlocks.RespWebDesignV9]: ResponsiveDesign,
  [SuperBlocks.JsV9]: JavaScriptIcon,
  [SuperBlocks.FrontEndDevLibsV9]: ReactIcon,
@@ -61,6 +61,7 @@
 }

 .block-label-exam,
+.block-label-math,
 .block-label-editors {
  border-color: var(--quaternary-color);
  color: var(--quaternary-color);
@@ -0,0 +1,38 @@
+---
+id: 699e8ca68f18cf77dfce5c27
+title: Difference Quotient
+challengeType: 11
+videoId: D5ajV73gC1k
+dashedName: difference-quotient
+---
+
+# --description--
+
+In this video, you will learn about the difference quotient.
+
+# --questions--
+
+## --text--
+
+What is a secant line?
+
+## --answers--
+
+A line that is always parallel to the x-axis.
+
+---
+
+A vertical line that intersects the y-axis.
+
+---
+
+A line that stretches between two points on the graph of a function.
+
+---
+
+A line that touches the graph of a function at exactly one point.
+
+## --video-solution--
+
+3
+
@@ -0,0 +1,39 @@
+---
+id: 699e85648f18cf77dfce5c23
+title: Ellipses
+challengeType: 11
+videoId: AwBM2AMwfu8
+dashedName: ellipses
+---
+
+# --description--
+
+In this video, you will learn about ellipses, their standard equations, and how to identify their key features.
+
+# --questions--
+
+## --text--
+
+What is an ellipse?
+
+## --answers--
+
+The set of points such that the sum of the distances from two fixed points is constant.
+
+---
+
+The set of points such that the distance from one fixed point is constant.
+
+---
+
+The set of points such that the product of the distances from two fixed points is constant.
+
+---
+
+The set of points equidistant from a line and a point.
+
+## --video-solution--
+
+1
+
+
@@ -0,0 +1,38 @@
+---
+id: 699e85688f18cf77dfce5c24
+title: Hyperbolas
+challengeType: 11
+videoId: rQnuydK6bBE
+dashedName: hyperbolas
+---
+
+# --description--
+
+In this video, you will learn about hyperbolas.
+
+# --questions--
+
+## --text--
+
+What is a hyperbola?
+
+## --answers--
+
+The set of points such that the distance from one fixed point is constant.
+
+---
+
+A set of points such that the difference of the distances from two fixed points is constant.
+
+---
+
+The set of points such that the sum of the distances from two fixed points is constant.
+
+---
+
+The set of points equidistant from a line and a point.
+
+## --video-solution--
+
+2
+
@@ -0,0 +1,38 @@
+---
+id: 699e85568f18cf77dfce5c20
+title: Law of Cosines - Old Version
+challengeType: 11
+videoId: 3BMPsNLtcmA
+dashedName: law-of-cosines-old-version
+---
+
+# --description--
+
+In this video, you will continue to learn about the Law of Cosines.
+
+# --questions--
+
+## --text--
+
+How many forms can the Law of Cosines be written in?
+
+## --answers--
+
+6
+
+---
+
+1
+
+---
+
+2
+
+---
+
+3
+
+## --video-solution--
+
+4
+
@@ -0,0 +1,40 @@
+---
+id: 699e85518f18cf77dfce5c1f
+title: Law of Cosines
+challengeType: 11
+videoId: KGF52g-s4Rs
+dashedName: law-of-cosines
+---
+
+# --description--
+
+In this video, you will learn about the Law of Cosines.
+
+# --questions--
+
+## --text--
+
+What is the Law of Cosines?
+
+## --answers--
+
+For any triangle with sides of length a, b, and c, and angle C opposite side c, the Law of Cosines states that `c^2 = a^2 + b^2 + 2ab * cos(C)`.
+
+---
+
+For any triangle with sides of length a, b, and c, and angle C opposite side c, the Law of Cosines states that `c = a + b - 2 * cos(C)`.
+
+
+---
+
+For any triangle with sides of length a, b, and c, and angle C opposite side c, the Law of Cosines states that `c^2 = a^2 + b^2 - 2ab * cos(C)`.
+
+---
+
+For any triangle with sides of length a, b, and c, and angle C opposite side c, the Law of Cosines states that `c = a * b * 2 * cos(C)`.
+
+## --video-solution--
+
+3
+
+
@@ -0,0 +1,39 @@
+---
+id: 699e855a8f18cf77dfce5c21
+title: Law of Sines
+challengeType: 11
+videoId: Arm0baqLKTo
+dashedName: law-of-sines
+---
+
+# --description--
+
+In this video, you will learn about the Law of Sines.
+
+# --questions--
+
+## --text--
+
+What can the Law of Sines be used to find?
+
+## --answers--
+
+To solve triangles that are right triangles.
+
+---
+
+To solve triangles that are not necessarily right triangles.
+
+---
+
+To solve triangles that are equilateral triangles.
+
+---
+
+To solve triangles that are isosceles triangles.
+
+## --video-solution--
+
+2
+
+
@@ -0,0 +1,38 @@
+---
+id: 699e855e8f18cf77dfce5c22
+title: Parabolas - Vertex, Focus, Directrix
+challengeType: 11
+videoId: fAXpgprNFq0
+dashedName: parabolas-vertex-focus-directrix
+---
+
+# --description--
+
+In this video, you will learn about special forms for equations of parabolas, and how to find the vertex, focus, and directrix of a parabola.
+
+# --questions--
+
+## --text--
+
+Which of the following is a valid form for the equation of a parabola?
+
+## --answers--
+
+`x - h = 4p(y - k)^2`
+
+---
+
+`y^2 - k^2 = 4p(x - h)`
+
+---
+
+`(y - k)^2 = 4p(x - h) `
+
+---
+
+`y - k = 4p(x - h)^2`
+
+## --video-solution--
+
+3
+
@@ -0,0 +1,39 @@
+---
+id: 699e85718f18cf77dfce5c26
+title: Parametric Equations
+challengeType: 11
+videoId: VP5KJr2giwI
+dashedName: parametric-equations
+---
+
+# --description--
+
+In this video, you will learn about parametric equations.
+
+# --questions--
+
+## --text--
+
+What is a cartesian equation for a curve? 
+
+## --answers--
+
+An equation in terms of r and θ that describes a curve.
+
+---
+
+An equation in terms of x and y that describes a curve.
+
+---
+
+An equation that only gives the slope of a curve at each point.
+
+---
+
+An equation in terms of distance from a fixed point only.
+
+## --video-solution--
+
+2
+
+
@@ -0,0 +1,38 @@
+---
+id: 699e856c8f18cf77dfce5c25
+title: Polar Coordinates
+challengeType: 11
+videoId: T8_EJkpyPvM
+dashedName: polar-coordinates
+---
+
+# --description--
+
+In this video, you will learn about polar coordinates.
+
+# --questions--
+
+## --text--
+
+What are polar coordinates?
+
+## --answers--
+
+Coordinates represented as (θ, φ), where θ is the angle from the y-axis and φ is the angle from the x-axis.
+
+---
+
+Coordinates represented as (r, s), where r is the distance from the origin and s is the slope of the line from the origin.
+
+---
+
+Coordinates represented as (x, y), where x and y are distances along the horizontal and vertical axes.
+
+---
+
+Coordinates represented as (r, θ), where r is the distance from the origin and θ is the angle from the positive x-axis.
+
+## --video-solution--
+
+4
+
@@ -0,0 +1,39 @@
+---
+id: 699e854b8f18cf77dfce5c1e
+title: Solving Right Triangles
+challengeType: 11
+videoId: AkRnIZDdq04
+dashedName: solving-right-triangles
+---
+
+# --description--
+
+In this video, you will learn how to solve right triangles. 
+
+# --questions--
+
+## --text--
+
+What does it mean to solve a right triangle?
+
+## --answers--
+
+To solve a right triangle means to find the area of the triangle only.
+
+---
+
+To solve a right triangle means to find only the length of the hypotenuse.
+
+---
+
+To solve a right triangle means to find the lengths of all sides and the measures of all angles.
+
+---
+
+To solve a right triangle means to draw the triangle without calculating any sides or angles.
+
+## --video-solution--
+
+3
+
+
@@ -0,0 +1,38 @@
+---
+id: 699e54288f18cf77dfce5c0a
+title: Angles and Their Measures
+challengeType: 11
+videoId: Ycu5Xn5rFuc
+dashedName: angles-and-their-measures
+---
+
+# --description--
+
+In this video, you will learn about the different ways to describe angles.
+
+# --questions--
+
+## --text--
+
+How are angles usually measured?
+
+## --answers--
+
+They are measured by lines or curves.
+
+---
+
+They are measured by degrees or radians.
+
+---
+
+They are measured by feet or meters.
+
+---
+
+They are measured by miles or kilometers.
+
+## --video-solution--
+
+2
+
@@ -0,0 +1,38 @@
+---
+id: 699e56b58f18cf77dfce5c0b
+title: Arclength and Areas of Sectors
+challengeType: 11
+videoId: hNtpuLx5i6Y
+dashedName: arclength-and-areas-of-sectors
+---
+
+# --description--
+
+In this video, you will learn about arcs, sectors and areas of sectors. 
+
+# --questions--
+
+## --text--
+
+What is a sector?
+
+## --answers--
+
+A wedge of pi for a circle.
+
+---
+
+A line that cuts a circle into two equal halves.
+
+---
+
+The distance around the outside of a circle.
+
+---
+
+The center point of a circle.
+
+## --video-solution--
+
+1
+
@@ -0,0 +1,39 @@
+---
+id: 699e56ba8f18cf77dfce5c0c
+title: Linear and Radial Speed
+challengeType: 11
+videoId: nsZvoNqWCMo
+dashedName: linear-and-radial-speed
+---
+
+# --description--
+
+In this video, you will learn about linear and radial speed for rotating circles.
+
+# --questions--
+
+## --text--
+
+What is linear speed?
+
+## --answers--
+
+The number of rotations completed in one minute.
+
+---
+
+The distance from the center of a circle to its edge.
+
+---
+
+The distance a point travels in a unit of time.
+
+---
+
+The angle a point rotates through in a unit of time.
+
+## --video-solution--
+
+3
+
+
@@ -0,0 +1,37 @@
+---
+id: 699e0342138be64fa313138c
+title: Even and Odd Functions
+challengeType: 11
+videoId: OCGl-6nrCtM
+dashedName: even-and-odd-functions
+---
+
+# --description--
+
+In this video, you will learn about even and odd functions.
+
+# --questions--
+
+## --text--
+
+What makes a graph symmetric with respect to the origin?
+
+## --answers--
+
+If it has a 30 degree rotational symmetry about the origin.
+
+---
+
+If it has a 180 degree rotational symmetry about the origin.
+
+---
+
+If it has a 90 degree rotational symmetry about the origin.
+
+---
+
+If it has a 360 degree rotational symmetry about the origin.
+
+## --video-solution--
+
+2
@@ -0,0 +1,37 @@
+---
+id: 699dfa14138be64fa3131389
+title: Functions
+challengeType: 11
+videoId: qyuFN2AKCBw
+dashedName: functions
+---
+
+# --description--
+
+Instructor Dr. Linda Green, a lecturer at the University of North Carolina at Chapel Hill, will teach you the basics of functions.
+
+# --questions--
+
+## --text--
+
+What is the domain of a function?
+
+## --answers--
+
+All possible a-values.
+
+---
+
+All possible y-values.
+
+---
+
+All possible x-values.
+
+---
+
+All possible z-values.
+
+## --video-solution--
+
+3
@@ -0,0 +1,37 @@
+---
+id: 699e0333138be64fa313138a
+title: Increasing and Decreasing Functions
+challengeType: 11
+videoId: GRYrrT_aQ1U
+dashedName: increasing-and-decreasing-functions
+---
+
+# --description--
+
+In this video, you will learn about increasing and decreasing functions on a graph.
+
+# --questions--
+
+## --text--
+
+What is an increasing function?
+
+## --answers--
+
+This is where the x values are increasing and the y values are increasing.
+
+---
+
+This is where the x values are increasing and the y values are decreasing.
+
+---
+
+This is where the x values are decreasing and the y values are increasing.
+
+---
+
+This is where the x values are decreasing and the y values are decreasing.
+
+## --video-solution--
+
+1
@@ -0,0 +1,37 @@
+---
+id: 699e0359138be64fa3131390
+title: Inverse Functions
+challengeType: 11
+videoId: f9ph7m0zgD0
+dashedName: inverse-functions
+---
+
+# --description--
+
+In this video, you will learn about inverse functions.
+
+# --questions--
+
+## --text--
+
+Do all functions have inverse functions?
+
+## --answers--
+
+No
+
+---
+
+Yes
+
+---
+
+Only for functions with a finite domain.
+
+---
+
+Only for functions that are increasing or decreasing everywhere.
+
+## --video-solution--
+
+1
@@ -0,0 +1,37 @@
+---
+id: 699e033c138be64fa313138b
+title: Maximum and Minimum Values on a Graph
+challengeType: 11
+videoId: E1JSGpO8i3w
+dashedName: maximum-and-minimum-values-on-a-graph
+---
+
+# --description--
+
+In this video, you will learn about maximum and minimum values on a graph.
+
+# --questions--
+
+## --text--
+
+What is another name for maximum and minimum values on a graph?
+
+## --answers--
+
+Cosine maximums and minimum values.
+
+---
+
+Variable maximum and minimum values.
+
+---
+
+Sine maximum and minimum values.
+
+---
+
+Global maximum and minimum values.
+
+## --video-solution--
+
+4
@@ -0,0 +1,37 @@
+---
+id: 699e0353138be64fa313138f
+title: Piecewise Functions
+challengeType: 11
+videoId: C9hCmH9nj4o
+dashedName: piecewise-functions
+---
+
+# --description--
+
+In this video, you will learn about piecewise functions.
+
+# --questions--
+
+## --text--
+
+What is a piecewise function?
+
+## --answers--
+
+A function that is defined by multiple sub-functions on the y-axis.
+
+---
+
+A function that is defined by a single formula for all values of x.
+
+---
+
+A function that is defined by the x and y values of a set of points.
+
+---
+
+A function that is defined by multiple sub-functions.
+
+## --video-solution--
+
+4
@@ -0,0 +1,37 @@
+---
+id: 699e0347138be64fa313138d
+title: Toolkit Functions
+challengeType: 11
+videoId: 3DbEglxB1HY
+dashedName: toolkit-functions
+---
+
+# --description--
+
+In this video, you will learn about toolkit functions.
+
+# --questions--
+
+## --text--
+
+Which of the following is NOT an example of a toolkit function?
+
+## --answers--
+
+`y = |x|`
+
+---
+
+`y = x`
+
+---
+
+`y = << x`
+
+---
+
+`y = x^2`
+
+## --video-solution--
+
+3
@@ -0,0 +1,37 @@
+---
+id: 699e034d138be64fa313138e
+title: Transformations of Functions
+challengeType: 11
+videoId: xSPh80M3f84
+dashedName: transformations-of-functions
+---
+
+# --description--
+
+In this video, you will learn about transformations of functions.
+
+# --questions--
+
+## --text--
+
+Which of the following is a valid rule for a transformation of a function?
+
+## --answers--
+
+Numbers on the inside of the function result in a vertical shift.
+
+---
+
+Numbers on the outside of the function result in a horizontal shift.
+
+---
+
+A negative sign results in a reflection.
+
+---
+
+A negative sign results in a vertical shift.
+
+## --video-solution--
+
+3
@@ -0,0 +1,39 @@
+---
+id: 699e5bab8f18cf77dfce5c11
+title: Graphs of Sine and Cosine
+challengeType: 11
+videoId: OoP1Lav_i9A
+dashedName: graphs-sine-cosine
+---
+
+# --description--
+
+In this video, you will learn about the graphs of sine and cosine functions.
+
+# --questions--
+
+## --text--
+
+What is the amplitude of a sine or cosine function?
+
+## --answers--
+
+Vertical distance between the maximum point and the midline.
+
+---
+
+Horizontal distance between two consecutive peaks
+
+---
+
+The slope of the sine or cosine curve at the maximum point.
+
+---
+
+Vertical distance between two minimum points.
+
+## --video-solution--
+
+1
+
+
@@ -0,0 +1,39 @@
+---
+id: 699e5ba78f18cf77dfce5c10
+title: Properties of Trigonometric Functions
+challengeType: 11
+videoId: x0_G0dA02uU
+dashedName: properties-of-trig-functions
+---
+
+# --description--
+
+In this video, you will learn about the properties of trigonometric functions.
+
+# --questions--
+
+## --text--
+
+What is the Pythagorean property of trigonometric functions?
+
+## --answers--
+
+For any angle, the square of the sine of the angle minus the square of the cosine of the angle equals 1.
+
+---
+
+For any angle, the sine of the angle plus the cosine of the angle equals 1.
+
+---
+
+For any angle, the square of the sine of the angle plus the square of the cosine of the angle equals 1.
+
+---
+
+For any angle, the square of the tangent of the angle plus the square of the cosine of the angle equals 1.
+
+## --video-solution--
+
+3
+
+
@@ -0,0 +1,39 @@
+---
+id: 699e5b998f18cf77dfce5c0d
+title: Right Angle Trigonometry
+challengeType: 11
+videoId: j81PeMJaju0
+dashedName: right-angle-trigonometry
+---
+
+# --description--
+
+In this video, you will learn about common trig functions including sine, cosine, and tangent and how to calculate them for right triangles.
+
+# --questions--
+
+## --text--
+
+What is the sine of theta for a right triangle?
+
+## --answers--
+
+Adjacent over opposite
+
+---
+
+Opposite over hypotenuse
+
+---
+
+Hypotenuse over opposite
+
+---
+
+Adjacent over hypotenuse
+
+## --video-solution--
+
+2
+
+
@@ -0,0 +1,39 @@
+---
+id: 699e5b9e8f18cf77dfce5c0e
+title: Sine and Cosine of Special Angles
+challengeType: 11
+videoId: X0Bh-NiQ3KQ
+dashedName: sine-cosine-special-angles
+---
+
+# --description--
+
+In this video, you will learn how to find the sine and cosine of special angles, such as 30°, 45°, and 60°. 
+
+# --questions--
+
+## --text--
+
+What is the cosine of 45° for a right triangle with the hypotenuse of length 5?
+
+## --answers--
+
+`sqrt(3)/2`
+
+---
+
+`sqrt(5)/5`
+
+---
+
+`1/sqrt(2)`
+
+---
+
+`sqrt(2)/2`
+
+## --video-solution--
+
+4
+
+
@@ -0,0 +1,38 @@
+---
+id: 699e5ba28f18cf77dfce5c0f
+title: Unit Circle Definition of Sine and Cosine
+challengeType: 11
+videoId: zt4bkQc1nSw
+dashedName: unit-circle-definition-sine-cosine
+---
+
+# --description--
+
+In this video, you will learn how to use the unit circle to find the sine and cosine of angles. 
+
+# --questions--
+
+## --text--
+
+What is a unit circle?
+
+## --answers--
+
+A circle with a radius of 0 units.
+
+---
+
+A circle with a radius of 1 unit.
+
+---
+
+A circle with a radius of 2 units.
+
+---
+
+A circle with a radius of 0.5 units.
+
+## --video-solution--
+
+2
+
@@ -0,0 +1,39 @@
+---
+id: 699e71f58f18cf77dfce5c16
+title: Solving Basic Trig Equations
+challengeType: 11
+videoId: JfTpmqwIzzc
+dashedName: solving-basic-trig-equations
+---
+
+# --description--
+
+In this video, you will learn how to solve basic trigonometric equations.
+
+# --questions--
+
+## --text--
+
+What was the first step in solving the trig equation in the first example?
+
+## --answers--
+
+Isolating the cosine function.
+
+---
+
+Maximizing the cosine function.
+
+---
+
+Minimizing the cosine function.
+
+---
+
+Replacing the cosine function with the sine function.
+
+## --video-solution--
+
+1
+
+
@@ -0,0 +1,39 @@
+---
+id: 699e71f98f18cf77dfce5c17
+title: Solving Trig Equations that Require a Calculator
+challengeType: 11
+videoId: 8IwkABil9qQ
+dashedName: solving-trig-equations-that-require-a-calculator
+---
+
+# --description--
+
+In this video, you will learn how to solve trig equations that require a calculator. 
+
+# --questions--
+
+## --text--
+
+What is the main difference between solving basic trig equations with and without a calculator?
+
+## --answers--
+
+You can only solve sine and cosine equations with a calculator, not tangent equations.
+
+---
+
+Using a calculator gives only approximate solutions, while without a calculator you always get exact answers.
+
+---
+
+Solving without a calculator requires multiplying all angles by 2.
+
+---
+
+Using a calculator does not involve using the unit circle to find solutions.
+
+## --video-solution--
+
+4
+
+
@@ -0,0 +1,39 @@
+---
+id: 699e69db8f18cf77dfce5c12
+title: Graphs of Sinusoidal Functions
+challengeType: 11
+videoId: Jif_m8LkyMA
+dashedName: graphs-of-sinusoidal-functions
+---
+
+# --description--
+
+In this video, you will learn about the graphs of sinusoidal functions.
+
+# --questions--
+
+## --text--
+
+What are sinusoidal functions related to?
+
+## --answers--
+
+They are related to tangent and cotangent.
+
+---
+
+They are related to secant and cosecant.
+
+---
+
+They are related to tangent and secant.
+
+---
+
+They are related to sine and cosine.
+
+## --video-solution--
+
+4
+
+
@@ -0,0 +1,39 @@
+---
+id: 699e69e18f18cf77dfce5c13
+title: Graphs of Tan, Sec, Cot, Csc
+challengeType: 11
+videoId: -AGLDRcJ4hk
+dashedName: graphs-of-tan-sec-cot-csc
+---
+
+# --description--
+
+In this video, you will learn how to graph the tangent, secant, cotangent, and cosecant functions. 
+
+# --questions--
+
+## --text--
+
+What would be the slope when the angle is zero for the first example graph shown in the video?
+
+## --answers--
+
+1
+
+---
+
+2
+
+---
+
+0
+
+---
+
+-1
+
+## --video-solution--
+
+3
+
+
@@ -0,0 +1,39 @@
+---
+id: 699e69e58f18cf77dfce5c14
+title: Graphs of Transformations of Tan, Sec, Cot, Csc
+challengeType: 11
+videoId: 07CAThFU14c
+dashedName: graphs-of-transformations-of-tan-sec-cot-csc
+---
+
+# --description--
+
+In this video, you will learn how to graph the transformations of tangent, secant, cotangent, and cosecant functions.
+
+# --questions--
+
+## --text--
+
+What is the shape of the second graph shown in the video?
+
+## --answers--
+
+Secant graph.
+
+---
+
+Tangent graph.
+
+---
+
+Sinusoidal graph.
+
+---
+
+Cosecant graph.
+
+## --video-solution--
+
+2
+
+
@@ -0,0 +1,39 @@
+---
+id: 699e69ea8f18cf77dfce5c15
+title: Inverse Trig Functions
+challengeType: 11
+videoId: hlzdIVKJCdA
+dashedName: inverse-trig-functions
+---
+
+# --description--
+
+In this video, you will learn about inverse trig functions.
+
+# --questions--
+
+## --text--
+
+How can you find the graph of an inverse of a function?
+
+## --answers--
+
+Flipping the graph of the original function across the line `y = x * 2` and then across the line `y = x`.
+
+---
+
+Flipping the graph of the original function across the line `y = x` and then across the line `y = -x`.
+
+---
+
+Flipping the graph of the original function across the line `y = x`.
+
+---
+
+Flipping the graph of the original function across the line `y = -x`.
+
+## --video-solution--
+
+3
+
+
@@ -0,0 +1,39 @@
+---
+id: 699e782f8f18cf77dfce5c1a
+title: Angle Sum and Difference Formulas
+challengeType: 11
+videoId: cWSkoA9jshQ
+dashedName: angle-sum-and-difference-formulas
+---
+
+# --description--
+
+In this video, you will learn about the angle sum and difference formulas.
+
+# --questions--
+
+## --text--
+
+What is the exact value for `sin(105°)`?
+
+## --answers--
+
+`tan(60° + 45°) = (tan(60°) + tan(45°)) / (1 - tan(60°)tan(45°))`
+
+---
+
+`cos(15°) = cos(60°−45°) = cos(60°)cos(45°) + sin(60°)sin(45°) = (1/2)(√2/2) + (√3/2)(√2/2) = (√6 + √2)/4`
+
+---
+
+`sin(60°−45°)=sin(60°)cos(45°)−cos(60°)sin(45°)`
+
+---
+
+`sin(60° + 45°) = sin(60°)cos(45°) + cos(60°)sin(45°) = (√3/2)(√2/2) + (1/2)(√2/2) = (√6 + √2)/4`
+
+## --video-solution--
+
+4
+
+
@@ -0,0 +1,39 @@
+---
+id: 699e78398f18cf77dfce5c1c
+title: Double Angle Formulas
+challengeType: 11
+videoId: QMaQImbBe0M
+dashedName: double-angle-formulas
+---
+
+# --description--
+
+In this video, you will learn about the double angle formulas.
+
+# --questions--
+
+## --text--
+
+What is the double angle formula for `sin(2θ)`?
+
+## --answers--
+
+`sin(2θ) = 2 cos²(θ)`
+
+---
+
+`sin(2θ) = cos(2θ)`
+
+---
+
+`sin(2θ) = 2sin(θ)cos(θ)`
+
+---
+
+`sin(2θ) = sin²(θ) - cos²(θ)`
+
+## --video-solution--
+
+3
+
+
@@ -0,0 +1,39 @@
+---
+id: 699e783f8f18cf77dfce5c1d
+title: Half Angle Formulas
+challengeType: 11
+videoId: aJRfi6KrCcM
+dashedName: half-angle-formulas
+---
+
+# --description--
+
+In this video, you will learn about half angle formulas.
+
+# --questions--
+
+## --text--
+
+What is the half angle formula for `cos(θ/2)`?
+
+## --answers--
+
+`cos(θ/2) = (1 + cos(θ)) / 2`
+
+---
+
+`cos(θ/2) = ±√((1 + cos(θ)) / 2)`
+
+---
+
+`cos(θ/2) = ±√((1 - cos(θ)) / 2)`
+
+---
+
+`cos(θ/2) = √(1 - cos²(θ))`
+
+## --video-solution--
+
+2
+
+
@@ -0,0 +1,39 @@
+---
+id: 699e78348f18cf77dfce5c1b
+title: Proof of the Angle Sum Formulas
+challengeType: 11
+videoId: lSJAegqvosg
+dashedName: proof-of-the-angle-sum-formulas
+---
+
+# --description--
+
+In this video, you will learn about the proof of the angle sum formulas.
+
+# --questions--
+
+## --text--
+
+What is the angle sum formula for sine?
+
+## --answers--
+
+`sin(a + b) = sin(a) * cos(b) + cos(a) * sin(b)`
+
+---
+
+`cos(a + b) = cos(a) * cos(b) - sin(a) * sin(b)`
+
+---
+
+`tan(a + b) = (tan(a) + tan(b)) / (1 - tan(a) * tan(b))`
+
+---
+
+`sin(a + b) = sin(a) * cos(b) - cos(a) * sin(c)`
+
+## --video-solution--
+
+1
+
+
@@ -0,0 +1,39 @@
+---
+id: 699e782a8f18cf77dfce5c19
+title: Pythagorean Identities
+challengeType: 11
+videoId: C1i_FlxW_uE
+dashedName: pythagorean-identities
+---
+
+# --description--
+
+In this video, you will learn about the Pythagorean identities.
+
+# --questions--
+
+## --text--
+
+Which of the following is an example of a Pythagorean identity?
+
+## --answers--
+
+`sec^2(x) + tan^2(x) = 1`
+
+---
+
+`tan^2(x) + 1 = sec^2(x)`
+
+---
+
+`csc^2(x) + cot^2(x) = 1`
+
+---
+
+`cot^2(x) - 1 = csc^2(x)`
+
+## --video-solution--
+
+2
+
+
@@ -0,0 +1,39 @@
+---
+id: 699e78258f18cf77dfce5c18
+title: Trig Identities
+challengeType: 11
+videoId: m4rl9OE5XTY
+dashedName: trig-identities
+---
+
+# --description--
+
+In this video, you will learn about trigonometric identities.
+
+# --questions--
+
+## --text--
+
+Why is the second equation in the first example called an identity?
+
+## --answers--
+
+Its tangent and cotangent functions are equal.
+
+---
+
+Its cosine and secant functions are equal.
+
+---
+
+It holds all values of the variable.
+
+---
+
+It holds none of the values of the variable.
+
+## --video-solution--
+
+3
+
+
@@ -35,6 +35,7 @@ const superblocks = [
  '2022/responsive-web-design',
  'the-odin-project',
  'introduction-to-algorithms-and-data-structures',
+  'introduction-to-precalculus',
  'lab-survey-form',
  'html-and-accessibility',
  'computer-basics',
@@ -207,6 +207,7 @@ export const superBlockNames = {
  'learn-python-for-beginners': SuperBlocks.LearnPythonForBeginners,
  'introduction-to-algorithms-and-data-structures':
    SuperBlocks.IntroductionToAlgorithmsAndDataStructures,
+  'introduction-to-precalculus': SuperBlocks.IntroductionToPrecalculus,
  'lab-survey-form': SuperBlocks.LabSurveyForm,
  'html-and-accessibility': SuperBlocks.HtmlAndAccessibility,
  'computer-basics': SuperBlocks.ComputerBasics,
@@ -0,0 +1,50 @@
+{
+  "name": "Advanced Trig & Conics",
+  "blockLabel": "lecture",
+  "blockLayout": "challenge-list",
+  "isUpcomingChange": false,
+  "dashedName": "advanced-trig-conics",
+  "helpCategory": "General",
+  "challengeOrder": [
+    {
+      "id": "699e854b8f18cf77dfce5c1e",
+      "title": "Solving Right Triangles"
+    },
+    {
+      "id": "699e85518f18cf77dfce5c1f",
+      "title": "Law of Cosines"
+    },
+    {
+      "id": "699e85568f18cf77dfce5c20",
+      "title": "Law of Cosines - Old Version"
+    },
+    {
+      "id": "699e855a8f18cf77dfce5c21",
+      "title": "Law of Sines"
+    },
+    {
+      "id": "699e855e8f18cf77dfce5c22",
+      "title": "Parabolas - Vertex, Focus, Directrix"
+    },
+    {
+      "id": "699e85648f18cf77dfce5c23",
+      "title": "Ellipses"
+    },
+    {
+      "id": "699e85688f18cf77dfce5c24",
+      "title": "Hyperbolas"
+    },
+    {
+      "id": "699e856c8f18cf77dfce5c25",
+      "title": "Polar Coordinates"
+    },
+    {
+      "id": "699e85718f18cf77dfce5c26",
+      "title": "Parametric Equations"
+    },
+    {
+      "id": "699e8ca68f18cf77dfce5c27",
+      "title": "Difference Quotient"
+    }
+  ]
+}
@@ -0,0 +1,22 @@
+{
+  "name": "Angles and Circular Motion",
+  "blockLabel": "lecture",
+  "blockLayout": "challenge-list",
+  "isUpcomingChange": false,
+  "dashedName": "angles-and-circular-motion",
+  "helpCategory": "General",
+  "challengeOrder": [
+    {
+      "id": "699e54288f18cf77dfce5c0a",
+      "title": "Angles and Their Measures"
+    },
+    {
+      "id": "699e56b58f18cf77dfce5c0b",
+      "title": "Arclength and Areas of Sectors"
+    },
+    {
+      "id": "699e56ba8f18cf77dfce5c0c",
+      "title": "Linear and Radial Speed"
+    }
+  ]
+}
@@ -0,0 +1,42 @@
+{
+  "name": "Function Basics",
+  "blockLabel": "lecture",
+  "blockLayout": "challenge-list",
+  "isUpcomingChange": false,
+  "dashedName": "function-basics",
+  "helpCategory": "General",
+  "challengeOrder": [
+    {
+      "id": "699dfa14138be64fa3131389",
+      "title": "Functions"
+    },
+    {
+      "id": "699e0333138be64fa313138a",
+      "title": "Increasing and Decreasing Functions"
+    },
+    {
+      "id": "699e033c138be64fa313138b",
+      "title": "Maximums and Minimums on Graphs"
+    },
+    {
+      "id": "699e0342138be64fa313138c",
+      "title": "Even and Odd Functions"
+    },
+    {
+      "id": "699e0347138be64fa313138d",
+      "title": "Toolkit Functions"
+    },
+    {
+      "id": "699e034d138be64fa313138e",
+      "title": "Transformations of Functions"
+    },
+    {
+      "id": "699e0353138be64fa313138f",
+      "title": "Piecewise Functions"
+    },
+    {
+      "id": "699e0359138be64fa3131390",
+      "title": "Inverse Functions"
+    }
+  ]
+}
@@ -0,0 +1,30 @@
+{
+  "name": "Right Triangle Trigonometry",
+  "blockLabel": "lecture",
+  "blockLayout": "challenge-list",
+  "isUpcomingChange": false,
+  "dashedName": "right-triangle-trigonometry",
+  "helpCategory": "General",
+  "challengeOrder": [
+    {
+      "id": "699e5b998f18cf77dfce5c0d",
+      "title": "Right Angle Trigonometry"
+    },
+    {
+      "id": "699e5b9e8f18cf77dfce5c0e",
+      "title": "Sine and Cosine of Special Angles"
+    },
+    {
+      "id": "699e5ba28f18cf77dfce5c0f",
+      "title": "Unit Circle Definition of Sine and Cosine"
+    },
+    {
+      "id": "699e5ba78f18cf77dfce5c10",
+      "title": "Properties of Trig Functions"
+    },
+    {
+      "id": "699e5bab8f18cf77dfce5c11",
+      "title": "Graphs of Sine and Cosine"
+    }
+  ]
+}
@@ -0,0 +1,18 @@
+{
+  "name": "Solving Trig Equations",
+  "blockLabel": "lecture",
+  "blockLayout": "challenge-list",
+  "isUpcomingChange": false,
+  "dashedName": "solving-trig-equations",
+  "helpCategory": "General",
+  "challengeOrder": [
+    {
+      "id": "699e71f58f18cf77dfce5c16",
+      "title": "Solving Basic Trig Equations"
+    },
+    {
+      "id": "699e71f98f18cf77dfce5c17",
+      "title": "Solving Trig Equations that Require a Calculator"
+    }
+  ]
+}
@@ -0,0 +1,26 @@
+{
+  "name": "Trig Graphs & Inverses",
+  "blockLabel": "lecture",
+  "blockLayout": "challenge-list",
+  "isUpcomingChange": false,
+  "dashedName": "trig-graphs-inverses",
+  "helpCategory": "General",
+  "challengeOrder": [
+    {
+      "id": "699e69db8f18cf77dfce5c12",
+      "title": "Graphs of Sinusoidal Functions"
+    },
+    {
+      "id": "699e69e18f18cf77dfce5c13",
+      "title": "Graphs of Tan, Sec, Cot, Csc"
+    },
+    {
+      "id": "699e69e58f18cf77dfce5c14",
+      "title": "Graphs of Transformations of Tan, Sec, Cot, Csc"
+    },
+    {
+      "id": "699e69ea8f18cf77dfce5c15",
+      "title": "Inverse Trig Functions"
+    }
+  ]
+}
@@ -0,0 +1,34 @@
+{
+  "name": "Trig Identities & Formulas",
+  "blockLabel": "lecture",
+  "blockLayout": "challenge-list",
+  "isUpcomingChange": false,
+  "dashedName": "trig-identities-formulas",
+  "helpCategory": "General",
+  "challengeOrder": [
+    {
+      "id": "699e78258f18cf77dfce5c18",
+      "title": "Trig Identities"
+    },
+    {
+      "id": "699e782a8f18cf77dfce5c19",
+      "title": "Pythagorean Identities"
+    },
+    {
+      "id": "699e782f8f18cf77dfce5c1a",
+      "title": "Angle Sum and Difference Formulas"
+    },
+    {
+      "id": "699e78348f18cf77dfce5c1b",
+      "title": "Proof of the Angle Sum Formulas"
+    },
+    {
+      "id": "699e78398f18cf77dfce5c1c",
+      "title": "Double Angle Formulas"
+    },
+    {
+      "id": "699e783f8f18cf77dfce5c1d",
+      "title": "Half Angle Formulas"
+    }
+  ]
+}
@@ -40,6 +40,7 @@
    "html-forms-and-tables",
    "learn-python-for-beginners",
    "introduction-to-algorithms-and-data-structures",
+    "introduction-to-precalculus",
    "lab-survey-form",
    "html-and-accessibility",
    "computer-basics",
@@ -0,0 +1,11 @@
+{
+  "blocks": [
+    "function-basics",
+    "angles-and-circular-motion",
+    "right-triangle-trigonometry",
+    "trig-graphs-inverses",
+    "solving-trig-equations",
+    "trig-identities-formulas",
+    "advanced-trig-conics"
+  ]
+}
@@ -19,6 +19,7 @@ enum Topic {
  InformationSecurity = 'information-security',
  ComputerFundamentals = 'computer-fundamentals',
  ComputerScience = 'computer-science',
+  Math = 'math',
  Databases = 'databases',
  Bash = 'bash',
  Git = 'git',
@@ -202,6 +203,12 @@ export const catalog: Catalog[] = [
    hours: 6,
    topic: Topic.ComputerScience
  },
+  {
+    superBlock: SuperBlocks.IntroductionToPrecalculus,
+    level: Levels.Intermediate,
+    hours: 6,
+    topic: Topic.Math
+  },
  {
    superBlock: SuperBlocks.IntroductionToBash,
    level: Levels.Intermediate,
@@ -368,6 +368,7 @@ export const superBlockToCertMap: {
  [SuperBlocks.CssAnimations]: null,
  [SuperBlocks.LearnPythonForBeginners]: null,
  [SuperBlocks.IntroductionToAlgorithmsAndDataStructures]: null,
+  [SuperBlocks.IntroductionToPrecalculus]: null,
  [SuperBlocks.IntroductionToBash]: null,
  [SuperBlocks.IntroductionToSQLAndPostgreSQL]: null,
  [SuperBlocks.LearnBashScripting]: null,
@@ -67,6 +67,7 @@ export enum SuperBlocks {
  CssAnimations = 'css-animations',
  LearnPythonForBeginners = 'learn-python-for-beginners',
  IntroductionToAlgorithmsAndDataStructures = 'introduction-to-algorithms-and-data-structures',
+  IntroductionToPrecalculus = 'introduction-to-precalculus',
  IntroductionToBash = 'introduction-to-bash',
  IntroductionToSQLAndPostgreSQL = 'introduction-to-sql-and-postgresql',
  LearnBashScripting = 'learn-bash-scripting',
@@ -226,6 +227,7 @@ export const superBlockStages: StageMap = {
    SuperBlocks.CssAnimations,
    SuperBlocks.LearnPythonForBeginners,
    SuperBlocks.IntroductionToAlgorithmsAndDataStructures,
+    SuperBlocks.IntroductionToPrecalculus,
    SuperBlocks.IntroductionToBash,
    SuperBlocks.IntroductionToSQLAndPostgreSQL,
    SuperBlocks.LearnBashScripting,