Complementary Angles

Two acute angles are complementary if

Two acute angles are complementary if their sum is 90°. Examples include 30° and 60°, 70° and 20°, and x° and (90 − x)°.

The complement of an acute angle

The complement of an acute angle θ is (90 − θ)°. For example, the complement of 48° is 42°.

sin(90° − θ) = cos θ

sin(90° − θ) = cos θ and cos(90° − θ) = sin θ. In right triangle ABC with ∠B = 90° and ∠ACB = θ, the angle ∠CAB is 90° − θ, which leads to this identi

tan(90° − θ) = cot θ

tan(90° − θ) = cot θ and cot(90° − θ) = tan θ.

cosec(90° − θ) = sec θ

cosec(90° − θ) = sec θ and sec(90° − θ) = cosec θ.