M17 LE4 Sem2 09-10 - MATH 17 LE4 | 03.08.10 SHOW ALL...

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Unformatted text preview: MATH 17 LE4 | 03.08.10 SHOW ALL NECESSARY SOLUTIONS. WORK NEATLY. I. Modified True or False. Write TRUE if the statement is always true. Otherwise, change the underlined phrase/expression to make the statement always true. Show your computations. 2 pts each 1. P (−4) lies in Quadrant III. 2. The range of the function f ( x) = csc x is [−1, 1]. 3. The function g( x) = tan x is periodic with period 2π. 4. The function h( x) = sin x cos x is odd. 5. If the terminal side of an angle θ in standard position contains the point (−1, 5), then cot θ = −5. II. Do as indicated. 1. Find the exact value of the following. (a) cot (−165◦ ) 5π 13π cos (b) cos 24 24 2. Express csc 4 pts 4 pts 28π π as a circular function value of θ such that 0 ≤ θ ≤ . 5 4 1 = csc x − cot x. csc x + cot x π π 4. Gven f ( x) = 1 + 2sin x+ . 3 9 4 pts 5 pts 3. Prove: (a) Give the period, the amplitude, and the range of the function. 2 pts (b) Graph one cycle of the function. 5 pts 6 pts each III. Determine the following given that sin A = 1. cos 3 π and < A < π. 5 2 A 2 2. tan A − π 3 3. sin 3 A *END OF EXAM* Total: 50 points "Friendship is unnecessary, like philosophy, like art... It has no survival value; rather it is one of those things that give value to survival." -C.S. Lewis /ajdporlante 01.22.10/ 1 ...
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