Cofunction and even/odd identities · derivation ·proof
Where cos(−θ) = cos θ comes from
Numbers first. cos 30° = cos(−30°) = √3/2: the wave is symmetric about the y-axis.
cos(−θ) = cos θ
Building it step by step
- cos 30° = √3/2Special angle.
- cos(−30°) = √3/2Mirror point, same x-coordinate.
- cos(−θ) = cos θSymmetry of the graph about the y-axis.
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 cosine is even page.