Trigonify

Topics · 3 identities

Cofunction

Complementary-angle identities linking each function to its cofunction.

Cofunction identity: sin(π/2 − θ) = cos θ

sin⁡(π2−θ)=cos⁡θ\sin(\tfrac{\pi}{2} - \theta) = \cos\theta

The sine of an angle equals the cosine of its complement: sin(π/2 − θ) = cos θ. In a right triangle the two acute angles are complements, and one angle's opposite side is the other's adjacent side - which is where the "co" in cosine comes from.

Open identity

Cofunction identity: cos(π/2 − θ) = sin θ

cos⁡(π2−θ)=sin⁡θ\cos(\tfrac{\pi}{2} - \theta) = \sin\theta

The cosine of an angle equals the sine of its complement: cos(π/2 − θ) = sin θ. It is the mirror of the sine cofunction identity, and the reason the sine and cosine graphs are the same curve shifted by π/2.

Open identity

Cofunction identity: tan(π/2 − θ) = cot θ

tan⁡(π2−θ)=cot⁡θ\tan(\tfrac{\pi}{2} - \theta) = \cot\theta

Tangent and cotangent are cofunctions: tan(π/2 − θ) = cot θ. The same complementary-angle relationship holds for every function-and-cofunction pair - sine/cosine, tangent/cotangent, secant/cosecant.

Open identity