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What you should learn How to evaluate trigonometric functions of acute angles Section 5.2 Right Triangle Trigonometry Objective: In this lesson you learned how to evaluate trigonometric functions of acute angles and how to use the fundamental trigonometric identities. I. The Six Trigonometric Functions In the right triangle shown below, label the three sides of the triangle relative to the angle labeled θ as (a) the hypotenuse, (b) the opposite side, and (c) the adjacent side. Abbreviations of the six functions. • Using the lengths of these three sides, six ratios can be formed that define the following six trigonometric functions of the acute angle θ. • List the abbreviation for each trigonometric function. Definitions of the six functions. • Let θ be an acute angle of a right triangle. Define the six trigonometric functions of the angle θ using opp = the length of the side opposite θ, adj = the length of the side adjacent to θ, and hyp = the length of the hypotenuse. Definitions of the six functions. The cosecant function is the reciprocal of the _________ function. The cotangent function is the reciprocal of the __________ function. The secant function is the reciprocal of the ___________ function. Side opposite θ The Six Trigonometric Functions θ Side adjacent θ opp sin hyp adj cos hyp hyp csc opp hyp sec adj opp tan adj adj cot opp Example 1: • In the right triangle below, find sin θ, cos θ, and tan θ. Give the sines, cosines, and tangents of the following special angles: sin tan cos Cofunctions Cofunctions of complementary angles are equal ____________ . If θ is an acute angle, then: cos sin cot tan csc sec II. Trigonometric Identities Reciprocal Identities What you should learn How to use the fundamental trigonometric identities List two quotient identities: List three Pythagorean identities: sin cos 1 2 2 1 tan sec 2 2 1 cot c sc 2 2 III. Evaluating Trigonometric Functions with a Calculator • To evaluate the secant function with a calculator, . . . 1 sec cos What you should learn How to use a calculator to evaluate trigonometric functions Example 2: Use a calculator to evaluate (a) tan 35.4° (b) cos 3 Remember to change modes (a) = .7106630094 (b) = -.9899924966 IV. Applications Involving Right Triangles • What does it mean to “solve a right triangle?” • An angle of elevation is . . . • An angle of depression is . . .