Sullivan Precalculus: Section 5.3 Properties of the Trig Functions Objectives of this Section Determine the Domain and Range of the Trigonometric Functions Determine the Period of the Trigonometric Functions Determine the Signs of the Trigonometric Functions in a Given Quadrant Find the Values of the Trigonometric Functions Utilizing Fundamental Identities Use Even-Odd Properties to Find the Exact Value of the Trigonometric Functions

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

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

x y (a, b) a 0 r a > 0, b > 0, r > 0 a 0, r > 0 a > 0, b 0

I (+, +) All positive x y

Reciprocal Identities Quotient Identities

c b a

Even-Odd Properties