5.3 Properties of the Trigonometric Function

y (0, 1) P = (a, b) x (-1, 0) (1, 0) (0, -1)

The domain of the sine function is the set of all real numbers. The domain of the cosine function is the set of all real numbers. The domain of the tangent function is the set of all real numbers except odd multiples of The domain of the secant function is the set of all real numbers except odd multiples of

The domain of the cotangent function is the set of all real numbers except integral multiples of The domain of the cosecant function is the set of all real numbers except integral multiples of

RANGE OF THE TRIGONOMETRIC FUNCTIONS Let P = (a, b) be the point on the unit circle that corresponds to the angle . Then, -1 < a < 1 and -1 < b < 1.

If there is a smallest such number p, this smallest value is called the (fundamental) period of f.

Periodic Properties

Theorem Even-Odd Properties

Find the exact value of b) a) a) b)

Find the exact value of b) a) a) b)

Reciprocal Identities Quotient Identities

c b a

Theorem Complementary Angles Theorem Cofunctions of complementary angles are equal.