Pythagorean Trigonometric Identity
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High Quality Content by WIKIPEDIA articles! The Pythagorean trigonometric identity is a trigonometric identity expressing the Pythagorean theorem in terms of trigonometric functions. Along with the sum-of-angles formulae (see Angle sum and difference identities) it is the basic relation among the sin and cos functions from which all others may be derived. If the trigonometric functions are defined in terms of the unit circle, the proof is immediate: given an angle , there is a unique point P on the unit circle centered at the origin in the Euclidean plane at an angle from the x-axis, and cos ,...
High Quality Content by WIKIPEDIA articles! The Pythagorean trigonometric identity is a trigonometric identity expressing the Pythagorean theorem in terms of trigonometric functions. Along with the sum-of-angles formulae (see Angle sum and difference identities) it is the basic relation among the sin and cos functions from which all others may be derived. If the trigonometric functions are defined in terms of the unit circle, the proof is immediate: given an angle , there is a unique point P on the unit circle centered at the origin in the Euclidean plane at an angle from the x-axis, and cos , sin are respectively the x- and y-coordinates of P. By definition of the unit circle, the sum of the squares of these coordinates is 1, hence the identity.
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