Math120R: Precalculus Test 4 Review, Spring 2016
Sections 6.1-6.4, 7.1-7.5
Note: This study aid is intended to help you review for test 4. Do not expect this
review to be identical to the actual test 4 given in your class.
Multiple Choice Practice
1.
If the radius of a circle is 3 cm., then the measure of an angle that cuts an arc of length 6 cm
is:
(A) 120
2.
(B) 
(C) 2
(D) 30º
(E) 0.5
A 40 inch long pendulum swings through an arc of 20  in one second. How far does the tip
of the pendulum move in that second? Round your answer to two decimal places.
20 
40 in
(A) 2.22 inches
(B) 12.73 inches
(D) 25.13 inches
(E) 800.00 inches
(C) 13.96 inches
3.
Use the angle 37.4 to determine the exact value of x in the figure below.
x
37.4
15.6

(A) x  15.6 sin 37.4 
(B)

tan 37.4 
x
15.6


(C) x  15.6 cot 37.4 

cot 37.4 
(D) x 
15.6
(E)
4.




x  15.6 tan 37.4 

From the top of a 100 foot lighthouse, the angle of depression to a ship in the ocean is 9
degrees. How far is the ship from the base of the lighthouse? Assume that the base of the
lighthouse is at the level of the sea. Round your answer to the nearest one decimal place.
(A) 15.8 feet
(B) 265.2 feet
(C) 452.8 feet
(D) 631.4 feet
(E) 981.7 feet
3
5. Suppose the angle A terminates in Quadrant III and sin A =  .
5
(A) 
4
5
(B)
4
5
3
5
(C)
(D) 
3
5
Find cos A.
(E) None of these
6. Let  be an angle in standard position. The terminal side of  intersects the unit circle at
 2 21 
 ,

 5 5  . Find cot  .


(A)
7.
21
21
5
(B)
(C) 
1
5
(D) 
2
21
(E)  21
Suppose csc  0 and tan   0 . In which quadrant(s) could  terminate?
(A) Quadrants I and III only.
(B) Quadrant III only.
(C) Quadrant IV only.
(D) Quadrants II and III only.
(E)
Quadrant II only.
8. Suppose the angle A terminates in Quadrant II and sec A  
(A)
3
4
(B) 
3
4
(C)
4
3
(D) 
4
3
5
. Find tan A.
4
(E) None of these
9. Find z as a degree measure rounded to one decimal place.
4 cm
3 cm
z
(A) 41.4o
(B) 48.6 o
(C) 36.9 o

(D) 53.1 o
(E) None of these

Simplify the expression sin tan 1 ( x) .
10.
(A)
1 x2
(B)
x
(C) x
1 x2

(D) 1  x 2
(E)
1 x2
x

Simplify the expression tan cos 1 (2 y ) .
11.
(A)
(D)
1 4y2
2y
1
(E)
1 4y2
12. Simplify the expression
(A) cot 2 
(B)
1 4y2
(C)
2y
1 4y2
1 2 y
2y
1
 1 completely.
cos 2 
(B) sec 2 
(C) 0
(D) tan 2 
(E) None of these
13. Simplify the expression sec cot  .
14.
15.
(A) 1
(B) tan 
(D) sin  cos
(E) csc 
Simplify the expression
(C) 1 cos
cos 2 x  sin 2 x
.
sec 2 x  tan 2 x
(A)  1
(B) 1
(D)  cos 2 x
(E) None of these
(C) sin 2 x
Suppose cos x  
1
1
and sin  y   where x terminates in Quadrant I and y
2
2
terminates in Quadrant II. Find sin( x  y ) .
(A)  1
(D)
1
2
(B) 
1
4
(E)
2
2
(C)
0
16.
Suppose sin  x  
1
1
and cos y   where x terminates in Quadrant I and y
3
3
terminates in Quadrant I. Find cos( x  y ) .
(A) 1
(D) 
(B)
7
9
17. Let sin x 

(D)
12
25
(C)
0
(E)  1
4
where x is in Quadrant II. Find sin( 2 x ) .
5
24
25
(A)
7
9
(B) 
12
25
(E)
24
25
(C)
6
5
18. Suppose x = n is a solution to the equation cos x  A , where 0  n 
Find another solution to the equation cos x  A .
(A) –n
(B) 2π – n
(C) π – n
(D) π + n
19. How many distinct solutions does the equation sin( 3x) 
(A) 1
(B) 3
(C) 6
(D) 12

2
.
(E) None of these
1
have on the interval [0,2 ) ?
2
(E) Infinitely many
Short Response Practice
1.
Find α and x. Approximate your answers to the nearest hundredth.
15 cm


20 cm
2.
x
Simplify each expression. Your final answer should be exact and should not contain
any trigonometric expression.
a. cos(tan 1 (2))
b. sin (cos 1 ( x))


c. cos 2 sin 1  y 
3.
Suppose tan   
7
, where  terminates in Quadrant II.
3
a. Find cos  . Give an exact answer.
b. Find cos( 2 ) . Give an exact answer.
4. Simplify the following trigonometric expressions:
a. cos tan   cot  
b.
1  sin t
cos t

cos t
1  sin t
tan 2 w  tan w
c.
1  sec 2 w
5. Solve for the indicated variable. Give exact answers.
a.
2 cos y  1 where 0  y  2
b. 2 sin  cos  
3
on the interval [0,2 )
2
c. 3sin 2 t  2 sin t  1 on the interval [0,2 )
d. sin( 2 )  cos   0 where 0    2
e. cos 2  
1
where 0    2
2
f. 2 cos 2 t  cos t  1 where 0  t  2
g. tan 3 x  tan x where 0  x  2
6. A swimming pool is three feet deep in the shallow end. The bottom of the pool has a
steady downward drop of 12  . If the pool is 50 feet long, how deep is it at the deep end?
Round the answer to 2 decimal places.
7. If a projectile is fired with velocity v0 at an angle of elevation  with the horizontal, then
the maximum height it reaches (in feet) is modeled by the function M   
Suppose that v0  400 feet/second.
v0 2 sin 2 
.
64
a. At what angle  should the projectile be fired so that the maximum height it
reaches is 2000 feet? Round your answer to the nearest tenth of a degree.
b. Is it possible for the projectile to reach a height of 3000 feet? Why or why not?