M17 LE4 Sem1 09-10

M17 LE4 Sem1 09-10 - 5 π< 2 A< π Moreover let B be an...

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Mathematics 17 First Semester AY 2009-2010 Fourth Long Exam 22 September 2009 General Instructions. Use only blue or black ballpen. Show all necessary solutions and box all final answers. I. MODIFIED TRUE OR FALSE. Write TRUE if the statement is true. Otherwise, provide a justification why the statement is false. 2 pts each 1. The graph of the function f ( x ) = sin 2 x + cos x is symmetric with respect to the origin. 2. The value of sin 16 is positive. 3. The angles - 465 and 17 π 12 are coterminal. 4. For all real numbers θ , P π 2 - θ = (sin θ, cos θ ), where P is the wrapping function. 5. The range of the function f ( x ) = csc ( x - π ) is R . II. Do as indicated. 3 pts each 1. Find the exact value of tan ( - 555 ) . 2. Find the exact value of sin π 24 cos 3 π 24 . 3. Express cot 73 π 13 as a trigonometric function value of θ such that 0 θ π 4 . 4. Given m = cos θ . Solve for cos 3 θ in terms of m . III. Let cos 2
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Unformatted text preview: . 5 π < 2 A < π . Moreover, let B be an angle in standard position whose terminal side contains the point C (1 ,-√ 2) . Determine the following. 5 pts each 1. P ( A ) and P ( B ), where P is the wrapping function 2. sin 2( A-B ) 3. cot 4 B IV. Prove the following identities. 5 pts each 1. tan 2 θ + sec 2 θ = cos θ + sin θ cos θ-sin θ 2. sin 2 x 4sec x-4tan x + sin 2 x 4sec x + 4tan x = sin x V. Graph f ( x ) =-2 π h sin ± πx 2-π 4 ²i + π 2 . Show only one cycle and indicate the period, amplitude, and the range of f . 5 pts *END OF EXAM* Total: 50 points “Don’t wish it was easier, wish you were better. Don’t wish for less problems, wish for more skills. Don’t wish for less challenge, wish for more wisdom.” MSNP /ajdporlante 09.14.09/ 1...
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