Trigonometry
Shape and Angle
The six trigonometric functions from the right triangle to the unit circle, their graphs, identities and equations, then the laws of sines and cosines, vectors, polar coordinates and complex numbers.
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Turning by Degrees and Radians
Unit 1 · Angles and Their Measure
0 of 12 units complete
- 1Unit 1Angles and Their Measure5 parts · about 18 min
Turning by Degrees and Radians
Spin an angle round the circle, land a skateboard trick, discover why radians are the natural unit, and use them to measure pizza slices and bicycle wheels.
- 2Unit 2Right Triangle Trigonometry5 parts · about 16 min
SOH-CAH-TOA Lab
Stretch and tilt a right triangle and find out what never changes. Then use it to measure kites, towers, and the size of the Earth.
- 3Unit 3The Unit Circle and Circular Functions5 parts · about 15 min
Around the Unit Circle
Free sine and cosine from triangles: a point going round a circle defines them for every angle, symmetry hands you every special value, and a Ferris wheel puts it to work.
- 4Unit 4Graphs of Sine and Cosine5 parts · about 14 min
Making Waves
Unroll the unit circle into the sine wave, then stretch, squeeze, flip and slide it until you can build any wave — tides, sound, daylight — from four numbers.
- 5Unit 5Graphs of the Other Trigonometric Functions5 parts · about 14 min
Asymptotes and Reciprocals
Tangent shoots off to infinity, secant hugs the cosine wave from outside, and a road sign turns out to be a tangent. See where the gaps come from and how to predict them.
- 6Unit 6Inverse Trigonometric Functions5 parts · about 14 min
Running Trig Backwards
Given a sine, find the angle — except there are infinitely many. Discover the restriction that makes the inverse work, use it on ladders and triangles, and dodge the traps it sets.
- 7Unit 7Trigonometric Identities5 parts · about 11 min
Identities You Can See
An identity is two expressions with the same graph. Find the Pythagorean identity with a slider, test guesses by overlaying graphs, catch a fake proof, then prove things for real.
- 8Unit 8Sum, Difference, and Multiple-Angle Formulas5 parts · about 13 min
Adding Angles
Is sin(A + B) just sin A + sin B? Test it, find the real formula, get exact values for angles like 15°, tame squares of sines, and hear the formula when two guitar strings beat.
- 9Unit 9Trigonometric Equations5 parts · about 14 min
Solving for the Angle
Every trig equation is a line crossing a wave. Count the crossings first, then find them exactly — by factoring, substituting, or reaching for an identity — and learn when daylight lasts exactly 12 hours.
- 10Unit 10Law of Sines and Law of Cosines5 parts · about 14 min
Solving Any Triangle
Drag a triangle around and watch one ratio refuse to change — the law of sines. Then meet its partner, the law of cosines, measure across a lake, and find the case with two answers.
- 11Unit 11Vectors and the Dot Product5 parts · about 15 min
Arrows with Directions
Drag arrows to add them, steer a boat across a current, measure the angle between two arrows with one multiplication, and split a force into the part that does the work.
- 12Unit 12Polar Coordinates and Complex Numbers5 parts · about 16 min
Spirals, Roses and Rotating Numbers
Describe points by distance and angle, draw flowers and hearts with one equation, and discover that multiplying complex numbers is just rotating and stretching.