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College Algebra/Analytic Geometry W1003 Section 003, Spring 2007 Final Exam Part II, Thomas D. Peters Name: May 8, 2007 Do all problems, in any order. Show your work. An answer alone may not receive full credit. No notes, texts, or calculators may be used on this part of the exam. Problem Possible Points Points Earned 1 10 2 10 3 10 4 5 5 10 6 10 7 10 8 10 TOTAL 75 1

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1. (10 points) Find the amplitude, period, and phase shift of the function y = - 1 2 sin 2 x - π 3 and graph one full period. 2. (10 points) Find the period and graph the function y = 3 csc π x + 1 2 . 3. (10 points) Verify the identity 1 + sin x 1 - sin x - 1 - sin x 1 + sin x = 4 tan x sec x . 4. (5 points) What is the exact value of sin 75
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Unformatted text preview: ? (you MUST justify your response–an answer alone will not receive any credit). 5. (10 points) Suppose sin x =-6 11 , x in quadrant III. (a) What is sin 2 x ? (b) Suppose further that 7 π 2 < x < 4 π . What is cos x 2 ? 6. (10 points) What is sin(sin-1 1 3 + tan-1 1 2 )? (You MUST justify your response–an answer alone will not receive any credit) 7. (10 points) Find all solutions of the equation 3 sin 2 x-7 sin x + 2 = 0. 8. (10 points) Solve the equation sin 2 x cos x + cos 2 x sin x = √ 3 / 2 Then ﬁnd all solutions in the interval [0 , 2 π ). 2...
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