5.3Properties of the Trigonometric

Function

(0, 1)

(-1, 0)

(0, -1)

(1, 0)

t radiansy

x

P = (a, b)

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 2 90 .

The domain of the secant function is the set of all real numbers except odd multiples of 2 90 .

The domain of the cotangent function is the set of all real numbers except integral multiples of 180 .

The domain of the cosecant function is the set of all real numbers except integral multiples of 180 .

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

RANGE OF THE TRIGONOMETRIC FUNCTIONS

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

a)

a)

b)

b)

Find the exact value of

a)

a) b)

b)

Reciprocal Identities

Quotient Identities

cb

a

90

Theorem Complementary Angles Theorem

Cofunctions of complementary angles are equal.