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Trigonometric Identities

Negative Angle Identities

Eight Fundamental Trigonometric Identities

Problems

Identities also exist to relate the value of a trigonometric function at a given angle to the value of that function at the opposite of the given angle. Here are these identities:

sin(- ≈íø) = - sin(≈íø)    

cos(- ≈íø) = cos(≈íø)    

tan(- ≈íø) = - tan(≈íø)    

csc(- ≈íø) = - csc(≈íø)    

sec(- ≈íø) = sec(≈íø)    

cot(- ≈íø) = - cot(≈íø)    

Any function f for which the equation f (- x) = - f (x) holds true is called an odd function. A function for which the equation f (- x) = f (x) holds true is called an even function. Sine and cosine are examples of odd and even functions, respectively. Odd and even functions, by definition, reflect themselves across the origin and y- axis, respectively. That is, a segment whose endpoints are f (x) and f (- x) of an odd function will always contain the origin, whereas a segment with the same endpoints on an even function will always be perpendicular to the y -axis.

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