 Complementary angles

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 nonshared 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^{2}A + sin^{2}B = 1, and cos^{2}A + cos^{2}B = 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
External links
 Animated demonstration  Interactive applet and explanation of the characteristics of complementary angles.
Categories: Elementary geometry
 Angle
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Complementary angles — Complementary Com ple*men ta*ry, a. Serving to fill out or to complete; as, complementary numbers. [1913 Webster] {Complementary colors}. See under {Color}. {Complementary angles} (Math.), two angles whose sum is 90[deg]. [1913 Webster] … The Collaborative International Dictionary of English
complementary angles — noun two angles whose sum is a right angle • Hypernyms: ↑angle * * * noun plural : two angles whose sum is a right angle * * * complementary angles UK US noun [plural] maths two angles that together form a right angle … Useful english dictionary
complementary angles — noun A pair of angles that sum to a right angle … Wiktionary
complementary angles — n. angles whose sum equals to 90 degrees … English contemporary dictionary
complementary angles — UK / US noun [plural] maths two angles that together form a right angle … English dictionary
Complementary — Com ple*men ta*ry, a. Serving to fill out or to complete; as, complementary numbers. [1913 Webster] {Complementary colors}. See under {Color}. {Complementary angles} (Math.), two angles whose sum is 90[deg]. [1913 Webster] … The Collaborative International Dictionary of English
Complementary colors — Complementary Com ple*men ta*ry, a. Serving to fill out or to complete; as, complementary numbers. [1913 Webster] {Complementary colors}. See under {Color}. {Complementary angles} (Math.), two angles whose sum is 90[deg]. [1913 Webster] … The Collaborative International Dictionary of English
complementary angle — ► NOUN ▪ either of two angles whose sum is 90° … English terms dictionary
complementary angle — n. either of two angles that together form a 90° angle … English World dictionary
complementary angle — Math. either of two angles that added together produce an angle of 90°. Cf. supplementary angle. * * * ˌcomplementary ˈangle [complementary angle] noun (geometry) either of two angles which together make 90° … Useful english dictionary