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Math 30-1 Trigonometric Equations: Lesson #4 Sum & Difference Identities Objective: By the end of this lesson, you will be able to: Question: Does sin sin sin ? Try it out for 60 and 30 ? Answer: The sum and difference identities for sine and cosine are: e.g. 1) Verify the identity cos cos cos sin sin for 2 and . 3 6 Math 30-1 Trigonometric Equations: Lesson #4 Tangent also has sum and difference identities, which can be derived from the sine and cosine sum and difference identities as follows: Tangent Sum Identity: sin tan , so: cos tan Substitute in the identities: Divide all terms by cos cos : Simplify: sin identity cos to switch back to tangent: Use the tan Similarly, the Tangent Difference Identity is: e.g. 2) Write the following as a single trigonometric function. Then write the exact value, if possible. tan 58 tan 77 a) b) cos 206 cos133 sin 206 sin 133 1 tan 58 tan 77 Math 30-1 Trigonometric Equations: Lesson #4 e.g. 3) Use sum and difference identities to simplify sin x . 2 3 5 3 B 2 , find the exact value of and cos B , where 0 A and 5 13 2 2 cos A B . e.g. 4) If cos A Sum and difference identities can also be used to determine exact values of some trig ratios that are not in the special triangles. To solve these problems, you need to find a combination of the memorized angles that will give a sum or difference of the angle in the question. It will always be a combination of angles with reference angles of: Math 30-1 Trigonometric Equations: Lesson #4 e.g. 5) Determine the exact value of: a) cos 255 b) tan Assignment: 12 p. 306-307 #1abd, 2abd, 6-10, 11c, 19, 20ab