Unit Circle Approach Properties of the Trigonometric Functions Section 5

Objectives Find the exact values of the trigonometric functions using the unit circle Know the domain and range of the trigonometric functions Use the periodic properties to find the exact values of the trigonometric functions Use even-odd properties to find the exact values of the trigonometric functions

Unit Circle Graph of x 2 + y 2 = 1 Radius = 1, Center (0, 0) Circumference = 2  Circular functions: trigonometric functions defined using unit circle Let (x, y) be any point that falls on the unit circle.

Circular Functions If θ = t radians, then sin t = ycsc t = 1/y cos t = xsec t = 1/x tan t = y/xcot t = x/y

Page 172 #9

Page 172 #15

DomainRange sin θ(-∞, ∞)[-1, 1] cos θ(-∞, ∞)[-1, 1] tan θθ ≠ mult. of π/2 (-∞, ∞) cot θθ ≠ mult. of π (-∞, ∞) sec θθ ≠ odd mult. of π/2 (-∞, 1] U [1, ∞) csc θθ ≠ mult. of π (-∞, 1] U [1, ∞)

Cosine and secant are even functions. The other four trigonometric functions are odd functions.

Pages (10-36 even)