Unit 4 Section 8 - . Example 4.8.5 Show that . Solution:...

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4.8 DOUBLE AND HALF MEASURE IDENTITIES Double Measure Identities Let be any real number. Then 1) 2) 3) Proof of 1) : Note that . Then by the sum identity for sine, we have . Therefore, . TIME TO THINK! Prove numbers 2) and 3). Example 4.8.1 Given that and is in quadrant II, find each of the following: a) Solution: From the Pythagorean relationships, and since is in quadrant II, then , and . . Therefore, . b) . c) . d) Since and , then . Example 4.8.2 Find an equivalent expression for each of the following: a) in terms of function values of only. Solution: . b) in terms of or , raised only to the first power. Solution: , since
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. Example 4.8.3 Prove/Verify the following identities: a) Proof: . b) Proof: . Example 4.8.4 Evaluate . Solution: Let . Then , terminates at QI and . . Since , then . Also, . Therefore,
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Unformatted text preview: . Example 4.8.5 Show that . Solution: Let and . Then and . Now, we only have to show that . . Example 4.8.6 Solve . Solution: Let and . Then and . The equation now is . Taking the cosine of both sides, we have . Checking: If , then , . Therefore, . Half-Measure Identities Let be any real number. Then 1) 2) 3) Proof of 1): Let be any real number. Then . Example 4.8.7 Find the exact value of . Solution: . Example 4.8.8 Find the value of sine, cosine and tangent of given that and terminates at QII. Solution: . Then, and are all positive. Why? . Example 4.8.9 Prove/Verify that . Proof: . Exercises: A. Find the value of , and , given: B. Prove/Verify: C. Find the values of sine, cosine and tangent of: D. Find the values of sine, cosine and tangent of: E. Prove/Verify: F. Prove...
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This note was uploaded on 05/13/2011 for the course MATH 17 taught by Professor Dikopaalam during the Spring '11 term at University of the Philippines Los Baños.

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Unit 4 Section 8 - . Example 4.8.5 Show that . Solution:...

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