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◦ )
2. Express csc 4 pts
4 pts 28π
as a circular function value of θ such that 0 ≤ θ ≤ .
= csc x − cot x.
csc x + cot x
4. Gven f ( x) = 1 + 2sin
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
and < A < π.
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."
/ajdporlante 01.22.10/ 1 ...
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- Spring '11
- Math, Periodic function, Continuous function, Inverse function, Leonhard Euler