Cofunction identity
SAT glossary · Math
Definition
sinθ = cos(90^circ - θ), because the two acute angles of a right triangle sum to 90^circ and one angle's opposite side is the other's adjacent side — the same side, renamed. Items phrase it 'if sin x = 0.6, what is cos(90^circ - x)?' and the answer is 0.6 with no computation.
Cofunction identity in plain English
In any right triangle, the two smaller (acute) angles always add up to exactly 90° — so if one angle is θ, the other is 90°-θ. Because of how sine and cosine are defined (using 'opposite' and 'adjacent' sides relative to an angle), the side that's 'opposite' one acute angle is the exact same side that's 'adjacent' to the other one. That's the whole secret behind the identity sinθ = cos(90°-θ) — it's really the same side being labeled from two different angles' points of view. So if a question tells you sin x = 0.6 and then asks for cos(90°-x), you don't need to calculate anything at all — it's automatically 0.6, because they're describing the exact same ratio.
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