Cofunction and even/odd identities · derivation ·proof

Where sin θ = cos(90° − θ) comes from

Measure from the other corner. The 'co-' in cosine means complement: cos θ started as 'the sine of the complement of θ'.

Building it step by step

1. sin of an angle = opp/hyp
   Definition.
2. Same ratio from the other acute angle
   Opposite and adjacent swap roles.
3. sin θ = cos(90° − θ)
   Name the swapped ratio.

How to recall it under pressure

Re-derive it from the first line rather than searching memory: start from sin(x) and do the one algebraic move the derivation above makes. If you need the statement itself, it is on the cofunction identity for sine page.

sampled at 800 random anglesSource: OpenStax Precalculus, Ch. 7 · Paul's Online Math Notes, Trig Cheat Sheet · revised 2026-09-26 ·how we check ·accuracy policy ·report an error