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This course will teach you 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.
By the end of this course, you’ll be a master at solving triangles, graphing trig functions in both Cartesian and polar coordinates, and applying trigonometric identities.
Overview
Syllabus
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- Introduction to Trigonometry: Start with sine and develop the beginnings of trigonometry.
- Exploring the Sine: Understand the sine function and how it gets used.
- Graphing the Sine: What does the graph of the sine function look like?
- Thinking in Polar: Use distance and angles to graph with circles and reveal new patterns.
- The Functions of Trigonometry: Learn the six basic trig functions in an intuitive way.
- Degrees and Radians: Get acquainted with two ways to measure an angle.
- Optional: Greek Letter Primer: Use this tutorial to get comfortable with Greek letters, which are common in trigonometry.
- Sine and Cosine: Explore the fundamental properties of the two fundamental trigonometry functions.
- The Unit Circle: Create a reference tool to help find the exact value of trig functions.
- Tangent: Learn about the third of trigonometry's main functions and apply it to solving for distances.
- Cosecant, Secant, Cotangent: Take reciprocals of the standard trig functions to get this alternate set of three.
- Measuring: Use trigonometry functions to solve for sides and angles.
- Solving Right Triangles: Apply what you've learned about sine, cosine, and tangent to find missing sides of triangles.
- Solving for Angles: Invert trigonometry functions to solve for angles instead of sides.
- Law of Sines: Calculate side lengths and angle measures on any triangle, not just right triangles.
- Law of Cosines: Learn a Law that works when Law of Sines doesn't
- Cartesian Graphing: Explore how trig graphs work on the traditional x-y plane.
- Trigonometry Graphs: What do the graphs of sine and cosine look like?
- Frequency and Phase Shift: Explore the basic attributes of waves.
- Adding Sine Curves: When you add two sine functions, sometimes it makes a mess and other times it just makes another sine.
- Other Trigonometry Function Graphs: Explore some unusual trigonometry graphs, including secant and cosecant.
- Trigonometry Graphs Problem Solving: Creatively apply your skills with trig graphs to solve some challenging puzzles.
- Inverse Trigonometry: Learn about and apply the inverse trigonometric functions: arcsine, arccosine, and others.
- Polar Graphing: Plot on a circle rather than a grid for some spectacular graphs.
- Polar Intro: Explore a new method of graphing that uses angle and distance as the two independent variables.
- Basic Polar Flowers: Make flowers using sine and cosine.
- More Flowers: Build up your skills with polar graphing by creating and understanding more complex flowers.
- Cardioids and Limacons: Investigate two special classes of polar graphs that look like hearts and beans.
- Polar Problem Solving: Strengthen your skills by solving some challenging polar graphing problems.
- Identities: Use substitutions to transform and simplify trig expressions.
- Reciprocal Identities: Launch into identities based on this set derived directly from the definitions of the six trig functions.
- Quotient Identities: Relate sine and cosine with tangent to enable changing between different trig functions.
- Even-Odd Identities: Apply symmetry as a method of simplification.
- Co-function Identities: Go back to right triangles and find a new useful property.
- Pythagorean Identities: Apply "a squared plus b squared equals c squared" to trigonometry.
- Problem Solving 1: Test out what you've learned in this mixture of problems.
- Sum and Difference Identities: Discover a clever method of handling addition and subtraction inside trig functions.
- Double-Angle Identities: Derive new identities for when an angle in a trig function is doubled.
- Half-Angle Identities: Explore scenarios where angle in a trig function is halved.
- Problem Solving 2: Bring together all you know about identities in this final challenge set.
