These and other fundamental identities are listed below. In Lesson 13.1 you used reciprocal identities to find the values of the cosecant, secant, and cotangent functions. Such equations are called trigonometric identities. cos x = 1.5 In the activity you may have discovered that some trigonometric equations are true for all values of x (in their domain). What do you notice about the graphs? Is the equation true for (a) no x-values, (b) some x-values, or (c) all x-values? (Set your calculator in radian mode and use ✢π ≤ x ≤ 2π and ✢ ≤ y ≤2.) 1. ACTIVITY Developing Concepts Investigating Trigonometric Identities Use a graphing calculator to graph each side of the equation in the same viewing window. REAL REAL LIFE LIFE Verifying Trigonometric Identities GOAL 1 USING TRIGONOMETRIC IDENTITIES In this lesson you will use trigonometric identities to evaluate trigonometric functions, simplify trigonometric expressions, and verify other identities. Why you should learn it To simplify real-life trigonometric expressions, such as the parametric equations that describe a carousel’s motion in Ex. GOAL 2 Use trigonometric identities to solve real-life problems, such as comparing the speeds at which people pedal exercise machines in Example 7. 14.3 What you should learn GOAL 1 Use trigonometric identities to simplify trigonometric expressions and to verify other identities. Prove that one trigonometric expression is equivalent to another so that we can replace.
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