Math 128
Exam II
Spring 2014
Name_____________________
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1. Find the terminal point P(x,y) on the unit circle determined by t =
(
)
(
√
.
)
2. Use the figure to approximate the terminal point determined by the real number t = 2.5
t = 2.5 lies approximately at the point (-0.8, 0.6)
3. Find the reference number for
a) t =
…….
b) t =
…….
4. Find the exact value of the following trigonometric functions at the given real numbers.
a)
b)
5. The terminal point (
√
Find tan t.
6. Suppose
) on the unit circle is determined by the real number t.
√
and the terminal point of t is in quadrant IV. What is
√
4
√65
9
7. Write
in terms of
if the terminal point of t is in quadrant II.
√
√
(but tan t is negative in quadrant II.
8. Find the exact value of cos(sin-1 5/13)
13
L
5
𝜃
N w

5
𝑎𝑛𝑑 𝑑𝑟𝑎𝑤 𝑎 𝑡𝑟𝑖𝑎𝑛𝑔𝑙𝑒
3
2
(𝑠𝑖𝑛 5/ 3)
𝜃
3
𝑠𝑖𝑛
12
(
9. Find the exact value of
( )) ………. =
10. Write an algebraic expression for tan(cos-1u).
L
1

u
√
𝑢
𝜃
N w
𝑐𝑜𝑠
(𝑐𝑜𝑠
(𝑢) 𝑎𝑛𝑑 𝑑𝑟𝑎𝑤 𝑎 𝑡𝑟𝑖𝑎𝑛𝑔𝑙𝑒
𝑢)
𝜃
√
𝑢
𝑢
11. A mass suspended from a spring is pulled down a distance of 4cm from its rest position. The
mass is released at time t = 0 and allowed to oscillate. If the mass returns to this position
after 1/2 second find an equation that describes its motion.
2
2
12. Graph y = sec(2x)
2
2
13. Graph y = -3cos(2x + /2) Amp__________; period____________; Phase shift__________