Math 153 Final Exam Extra Review Problems Worksheet Page 7
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848. A triangular lot has sides of length 4, 6, and 8 meters. Find the largest angle. Leave your answer
in exact form.
49.
49. Find the exact value of each: sin
, sin 15°, cos 22.5°
50. Give the domain and range of each (use appropriate notation):
= cos
,
= csc ,
= sec ,
= sin
,
= tan
51. From where he is perched in a tree, at a height of 20 ft., a hunter measures the angle of depression
to an ibex below to be 52°. How far is the ibex from the base of the tree?
52. From where I am standing (at point C) on one side of an arroyo, I choose points A and B, both on the
other side, which are 30 ft. apart. I measure
and
. Approximate the
BAC
56
ABC
23
distance from A to C. Leave your answer in exact form.
( − ) = tan
= sin ( − ) = −2 sin
53. Prove each a.
b. cos
+
c. 2 csc ( 2 ) tan = sec
= cos ( 2 ) . 2 cos ( 6 ) − 1 = cos(12 )
d.
54.. Suppose I know that cos ( 2 ) =
x in Quadrant II. Find sin ( ) , cos ( ) and tan ( ) .
55. Suppose I know that cos ( ) =
x in Quadrant I. Find sin ( 2 ) , cos ( 2 ) and tan ( 2 ) .
56 Rewrite the expressions in terms of only the first power of cosine
. cos (6 ) sin (6 )
. cos
57. Write the given expression in terms of x and y only.
−1
(cos
+ cot
)
(2 csc
)
a. cot(csc
x)
b.
c.
58. Find all solutions. Then, find all solutions in [0,2 ).
2
2
. 2sin θ + sin = 1
b. −2sin θ − 7cos − 2 = 0
c.
sin
t
7
cos
t
4
3
cos
t
. 3tan
− 1 = 0
e. tan (5θ) = tan(5 )
f. 3 sin 2 − 6 sin = 0
59. The height of a wave (in inches, after t seconds) is given by ( ) = 5
( 4 ) What’s the height
initially? What happens to the height as t increases? Explain your reasoning.
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