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PreCalculus Exam Review: 3rd Quarter
1) Determine the quadrant in which the terminal side of
7
an angle of
radians lies.
5
csc =
2.) Determine the quadrant in which the terminal side of
an angle of -355 lies.
7
, find tan .
4
21.) Find cos, given: sin = 
2
and tan > 0.
5
22.) If the point (8,-4) is on the terminal side of an angle
 in standard position, find sin.
3.) The smallest positive angle that is co-terminal to
 
20.) Given  as an acute angle of a right triangle, and
7
is:
6
23.) Find the reference angle for  = 115.
4.) Convert 440 to radian measure.
24) Determine the phase shift of the function:
7
5.) Convert
to degree measure.
12
6.) Find an angle that is complementary to
y 


8
.
7.) A central angle  of a circle with radius 4 inches
intercepts an arc 12 inches long.
Find  to the nearest tenth of a degree.
8.) Find the point (x, y) on the unit circle that
11
corresponds to the real number t 
.
6

 
9.) Evaluate: sin    . 10.) Evaluate: sec .
6
 3
19
13
11.) Evaluate: cos
. 12.) Evaluate: tan
.
6
6
13.) Use a calculator to evaluate: sec 14 to four
decimal places.
14.) Convert to (degree) decimal form:  11 32'15" .
15.) Find acute angle  if sin  = 0.9872.
16.) Determine the fundamental period of the
function: y 
1
2x
sin (   ) .
2
3
17.) To sketch the graph of the secant function, it is
convenient to first sketch the graph of which function?
18.) The fundamental period of the function
f ( x)  3 cot( x )
2
is?
19.) The horizontal (phase) shift of
g ( x)  2 sin (2 x 
[Type text]

2
) is?
1
x
sin (   ) .
3
2
25.) Determine the quadrant in which the terminal side
of a 
11
angle lies.
4
26.) Evaluate: arccos(  1 ).
2
27) State the vertical translation and the amplitude for
the graph: y = 4-3sin (2x +  ) ?
28.) Simplify:
cos( x)
sin(  x)
29.) Evaluate: arctan(  1 ).
30 and 31: Rewrite the given angle in terms of its
reference angle.
30.) cos 280o
31.) sin (-505o)
32. Find the smallest negative co-terminal angle for
 7
12
33.) A 15 foot ladder leans against a wall forming an
angle of elevation of 55o with the ground. How high on
the wall is the ladder?
34.) The angle of depression from a ship to a wreck on
the ocean floor is 7.8o. If the dept of the ocean at the
wreck in 925 ft, how far in miles should the ship sail so
that it is directly over the wreck?
35The angle of elevation from an observer on the
ground to an airplane flying at an altitude of 7.2
kilometers is 270. How far is the observer, in a straight
line, from the plane?
36. In a right triangle side a = 11 and c = 18. Determine
the measure of B.