Cofunction and even/odd identities · derivation ·proof
Where cos θ = sin(90° − θ) comes from
Shift the graph. The cosine curve is the sine curve moved left by π/2 — a fact used constantly in physics and AC circuits.
cos θ = sin(90° − θ)
Building it step by step
- Compare the graphs of sin and cosIdentical shape, offset by a quarter period.
- cos θ = sin(θ + π/2)Reading the offset one way.
- cos θ = sin(π/2 − θ)Reading it with the complement, which is the cofunction statement for acute angles.
How to recall it under pressure
Re-derive it from the first line rather than searching memory: start from cos(x) and do the one algebraic move the derivation above makes. If you need the statement itself, it is on the cofunction identity for cosine page.