Complementary angles

A pair of complementary angles because their measures add up to 90 degrees

In geometry, complementary angles are angles whose measures sum to 90°. If the two complementary angles are adjacent (i.e. have a common vertex and share just one side) their non-shared sides form a right angle.

In Euclidean geometry, the two acute angles in a right triangle are complementary, because the sum of internal angles of a triangle is 180 degrees, and the right angle itself accounts for ninety degrees.

The adjective complementary is from Latin complementum, associated with the verb complere, "to fill up". An acute angle is "filled up" by its complement to form a right angle.

Trigonometric ratios

The sine of an angle equals the cosine of its complementary angle. It is therefore true that, if angles A and B are complementary, $\sin^2A + \sin^2B = 1$, and $\cos^2A + \cos^2B = 1$.

The tangent of an angle equals the cotangent of its complementary angle. The tangents of complementary angles are reciprocals of each other.

The secant of an angle equals the cosecant of its complementary angle.

The prefix "co-" in the names of some trigonometric ratios refers to the word "complementary".

See also

• Supplementary angles
• Triangles

External links

• Animated demonstration - Interactive applet and explanation of the characteristics of complementary angles.