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Trigonometry

Explore trigonometry through identities, polar graphing, and solving triangles.

This course will teach you the all of the fundamentals of trigonometry, starting from square one: the basic idea of similar right triangles. In the first sequences in this course, you'll learn the definitions of the most common trigonometric functions from both a geometric and algebraic perspective.

In this course, you'll master trigonometry by solving challenging problems and interacting with animated graphs, not by relying on rote memorization. Additionally, you'll learn how to apply trigonometry in the contexts of measuring and manipulating sound waves and creating complex, artistic designs using polar graphing.

Interactive
quizzes

34

Concepts and
exercises

275+
  1. 1

    Introduction to Trigonometry

    Start with sine and develop the beginnings of trigonometry.

    1. Exploring the Sine

      Understand the sine function and how it gets used.

    2. Graphing the Sine

      What does the graph of the sine function look like?

    3. Thinking in Polar

      Use distance and angles to graph with circles and reveal new patterns.

  2. 2

    The Functions of Trigonometry

    Learn the six basic trig functions in an intuitive way.

    1. Included with
      Brilliant Premium

      Degrees and Radians

      Get acquainted with two ways to measure an angle.

    2. Included with
      Brilliant Premium

      Optional: Greek Letter Primer

      Use this tutorial to get comfortable with Greek letters, which are common in trigonometry.

    3. Included with
      Brilliant Premium

      Sine and Cosine

      Explore the fundamental properties of the two fundamental trigonometry functions.

    4. Included with
      Brilliant Premium

      The Unit Circle

      Create a reference tool to help find the exact value of trig functions.

  3. 3

    Measuring

    Use trigonometry functions to solve for sides and angles.

    1. Included with
      Brilliant Premium

      Solving Right Triangles

      Apply what you've learned about sine, cosine, and tangent to find missing sides of triangles.

    2. Included with
      Brilliant Premium

      Solving for Angles

      Invert trigonometry functions to solve for angles instead of sides.

    3. Included with
      Brilliant Premium

      Law of Sines

      Calculate side lengths and angle measures on any triangle, not just right triangles.

    4. Included with
      Brilliant Premium

      Law of Cosines

      Learn a Law that works when Law of Sines doesn't

  4. 4

    Cartesian Graphing

    Explore how trig graphs work on the traditional x-y plane.

    1. Included with
      Brilliant Premium

      Trigonometry Graphs

      What do the graphs of sine and cosine look like?

    2. Included with
      Brilliant Premium

      Frequency and Phase Shift

      Explore the basic attributes of waves.

    3. Included with
      Brilliant Premium

      Adding Sine Curves

      When you add two sine functions, sometimes it makes a mess and other times it just makes another sine.

    4. Included with
      Brilliant Premium

      Other Trigonometry Function Graphs

      Explore some unusual trigonometry graphs, including secant and cosecant.

  5. 5

    Polar Graphing

    Plot on a circle rather than a grid for some spectacular graphs.

    1. Included with
      Brilliant Premium

      Polar Intro

      Explore a new method of graphing that uses angle and distance as the two independent variables.

    2. Included with
      Brilliant Premium

      Basic Polar Flowers

      Make flowers using sine and cosine.

    3. Included with
      Brilliant Premium

      More Flowers

      Build up your skills with polar graphing by creating and understanding more complex flowers.

    4. Included with
      Brilliant Premium

      Cardioids and Limacons

      Investigate two special classes of polar graphs that look like hearts and beans.

  6. 6

    Identities

    Use substitutions to transform and simplify trig expressions.

    1. Included with
      Brilliant Premium

      Reciprocal Identities

      Launch into identities based on this set derived directly from the definitions of the six trig functions.

    2. Included with
      Brilliant Premium

      Quotient Identities

      Relate sine and cosine with tangent to enable changing between different trig functions.

    3. Included with
      Brilliant Premium

      Even-Odd Identities

      Apply symmetry as a method of simplification.

    4. Included with
      Brilliant Premium

      Co-function Identities

      Go back to right triangles and find a new useful property.