Trigonometry Summary

Algebra 2 · Axiom Academy

Trigonometric functions model periodic phenomena — from circular motion to sound waves and beyond. Every trig value comes from a point on the unit circle: is the x -coordinate, is the y -coordinate. Five special angles — — and their reflections have exact values worth memorizing cold. A sinusoid's shape is fully described by four numbers: amplitude, period, phase shift, and midline. The Pythagorean identity and the sum/double-angle formulas let you rewrite almost any trig expression into a more useful one. Because trig functions are periodic, an equation like has infinitely many solutions — always add the period to the reference solution. Core Concept Radians & the Unit Circle A radian is the angle that cuts off an arc equal in length to the radius. The unit circle — radius 1, centered at the origin — is the stage every trig idea plays out on. When to use: converting between degrees and radians — nearly every formula past this unit expects radians. Watch out for: dropping the — "2 radians" and " radians" are worlds apart. Core Concept Sine & Cosine as Coordinates Where the terminal side of angle meets the unit circle, cosine reads off the x -coordinate and sine reads off the y -coordinate. Every other trig fact follows from this one picture. When to use: finding the sign or exact value of sin/cos in any quadrant. Watch out for: mixing up which coordinate is which — cos = across, sin = up/down. Core Concept The Special Angles

This is the written version of the interactive lesson above. See the full Algebra 2 course.