Trigonometry

How to solve

Complementary angles swap sine and cosine: the opposite side for one acute angle is adjacent for its complement. That geometry is why sin(90° − θ) = cos θ and cos(90° − θ) = sin θ.

Steps

  1. Rewrite using sin(90° − θ) = cos θ or cos(90° − θ) = sin θ.
  2. Evaluate the resulting standard value if needed.

Example

Simplify sin(90° − 30°).

  1. Cofunction: sin(90° − 30°) = cos 30°.
  2. cos 30° = √3/2.

Answer: sqrt(3)/2

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