Trigonometric identities test

Graded Assignment MTH403B: Pre-Calculus/Trigonometry | Unit 4 | 4.4 Test Part 2 Name: Date: Test Trigonometric Identities Answer the following questions using what you’ve learned from this lesson. Write your responses in the space provided and turn the assignment in to your instructor. 1. Derive this identity from the sum and difference formulas for cosine: Score sin a sin b = (1 / 2)[cos(a – b) – cos(a + b)] Start with the right-hand side since it is more complex. Calculation Reason 2. Use the trigonometric subtraction formula for sine to verify this identity: sin((π / 2) – x) = cos x Calculation 3. Find the exact value of each of the following: a. cos(7π / 12) b. tan(17π / 12) c. sin(195°) d. cot(15°) Score Reason Score Answer: © 2009 K12 Inc. All rights reserved. Copying or distributing without K12’s written consent is prohibited. Page 1 of 2 Graded Assignment MTH403B: Pre-Calculus/Trigonometry | Unit 4 | 4.4 Test Part 2 4. Rewrite sin4 x so that it involves only the first power of cosine. Score Answer: 5. Prove the identity: Score (sin(2x) / sin x) – (cos(2x) / cos x) = sec x Answer: 6. Prove the identity: Score (cos x + cos y)2 + (sin x – sin y)2 = 2 + 2cos(x + y) Answer: 7. Solve these equations graphically on the interval [0, 2π]. Sketch the graph and list the Score solutions. a. sin x – 1 = cos x b. sin(2x) – 1 = tan x Answer: 8. Solve these equations: Score a. sin(x + (π / 4)) – sin(x – (π / 4) = 1 b. sin x cos x = √3 / 4 c. tan2 x – 3tan x + 2 = 0 Answer: Your Score © 2009 K12 Inc. All rights reserved. Copying or distributing without K12’s written consent is prohibited. ___ of 100 Page 2 of 2 ...
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