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Section 5.3 Trigonometric Functions of Any Angle Objective: In this lesson you learned how to evaluate trigonometric functions of any angle. Important Vocabulary Define each term or concept. • Reference angles • Period I. Introduction • Let θ be an angle in standard position with (x, y) a point on the terminal side of θ and r x y 0 2 2 Complete the following definitions of the trigonometric functions of any angle: opp sin hyp y r y x r x r y x x r x y r y • Name the quadrants in which the sine function is positive. • Name the quadrants in which the sine function is negative. • Name the quadrants in which the cosine function is positive. • Name the quadrants in which the cosine function is negative. • Name the quadrants in which the tangent function is positive. • Name the quadrants in which the tangent function is negative. What's your sign? Example 1 1 sin 2 Θ lies in either I or IV Important Vocabulary Define each term or concept. • Reference angles Let θ be an angle in standard position. Its reference angle is the acute angle θ’ formed by the terminal side and the horizontal axis (page 390) • Period II. Reference Angles Example 2 To find the value of a trigonometric function of any angle θ, . . . Example 3 III. Trigonometric Functions of Real Numbers • The sine function’s domain is ______________ and its range is ___________. • The cosine function’s domain is ____________ , and its range is _________ . • The period of the sine function is _______. The period of the cosine function is ___________ . Even and Odd • Which trigonometric functions are even functions? cos(t ) cos t sec(t ) sec t • Which trigonometric functions are odd functions? sin(t ) sin t csc(t ) csc t tan(t ) tan t cot(t ) cot t Homework • Pg 397: #1, 3, 7, 13-19 all, 21, 23, 24, 25, 27, 29, 33, 39-53 odd • Pg 398: #57, 59, 61, 65, 67, 69, 71, 75 77, 79, 81, 83, 85, 87, 91, 97, 99, 101, 103