After the unit circle and basic graphs, trigonometry becomes a toolkit: rewrite expressions, solve for angles, and model waves with amplitude, period, and midline. This guide builds on trigonometry basics.
The identity that never fails
sin²θ + cos²θ = 1
It is the unit circle equation x² + y² = 1 in trig clothes. The graph of sin² + cos² is a flat line at height 1.
Double-angle ideas
Sometimes a model needs sine or cosine of twice an angle:
sin(2θ) = 2 sinθ cosθ
cos(2θ) = cos²θ − sin²θ
These are algebra tools for simplifying and for solving equations.
Waves with amplitude and midline
y = A sin(Bx) + D stretches height by |A|, changes period via B, and shifts the middle line to y = D. Reading max and min from the formula is a core precalculus skill.