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Chapter 5 Section 5.3 Section 5.3: Sum and Difference Identities for Cosine I. Identities Identities We can use these identities in combination with special angle values to find the exact values for some “not so special” angles. Example 1 (Finding Exact Cosine Function Values): Find the exact value of each expression. a) cos 75 17 b) cos 12 Chapter 5 Section 5.3 c) cos173 cos83 sin173 sin83 II. Cofunction Identities Identities Note: We can replace 90 with . 2 Example 2 (Using Cofunction Identities to Find x): Find one value of x that satisfies each of the following. a) sec x csc62 b) tan x cot 54 Chapter 5 c) sin III. Section 5.3 7 cos x 6 Note: Because trigonometric (circular) functions are periodic, the solutions in Example 2 are not unique. We gave only one of infinitely many possibilities. Applying the Sum and Difference Identities If either angle A or B in the identities for cos(A + B) and cos(A – B) is a quadrantal angle, then the identity allows us to write the expression in terms of a single function of A or B. Example 3 (Rewriting an Expression): Write cos(90° + θ) as a trigonometric function of θ alone. Chapter 5 Section 5.3 Example 4 (Finding cos (s + t) Given Information About s and t): Suppose that cos s 15 , 17 sin t 24 , and both s and t are in quadrant IV. Find cos(s – t). 25 Example 5 (Verify an Identity): Verify that the following equation is an identity. sec x sec x