PreCalculus
Ch. 4 Review (4.1-4.7)
Name_______________________
Period _______
* Show work on the separate sheet of paper.
[1-2] State the amplitude, period, frequency, phase shift, vertical shift, and midline of each
function. Then graph two periods of the function. Be sure to label the scales on the axes of the
graph.
x


1. f ( x)  4 cos  5
2. g ( x)   sin  x  
2
2

[3-6] State the period and vertical asymptotes. Then sketch the graph of each function.

1
3. h( x)  tan( x  )
4. k ( x)  sec  2 x 
4
2

 x

5. y  2 csc  
6. j ( x)  2 cot  2 x  
3
3

[7-12] Find the exact values, if they exist.
1
7. arccos( )
2
3
10. tan 1 (tan )
2
9. sin 1 
8. tan 1 (1)
11. tan(arcsin
1
)
2
12. sin 1 (cos

6
)
[13-16] Solve # ABC.
13.
14.
15.
16.
A=30 , B=100 , a=15
A=38 , C=63 , b=15
a=7, b=10, c=5
C=40 , a=30, b=30
[17-18] Find the area of # ABC.
17. A=110 , b =21, c =18
18. a =25, b =23, c =14
19. Find two triangles for which A=49 , a =12, b =15.
[20-22] Find the Exact Values of the five remaining trigonometric functions of  .
20. tan  = 2, where sin  > 0 and cos  >0
21. cos  = -1/2, where sin  >0
22. sec  = √3 , where sin  < 0 and cos  > 0
[23-26] angle of elevation / depression problems
23. A building is 50 feet high. At a distance away from the building, an observer notices that the
angle of elevation to the top of the building is 41º. How far is the observer from the base of the
building?
24. An airplane is flying at a height of 2 miles above the ground. The distance along the ground
from the airplane to the airport is 5 miles. What is the angle of depression from the airplane to
the airport?
25. Eden is on vacation looking down into a deep canyon using binoculars. She sees Jane at the bottom
of the canyon with an angle of depression of 15o and sees Sarah with an angle of depression of 20o. The
canyon is 500 feet deep. Find the distance between Jane and Sarah.
26. A disabled jet can glide at an angle of depress of 11 degrees. If it starts the glide at an altitude
of 12000 ft, can it reach the landing strip that is 10 miles away? (1 mile = 5280 feet)
[27-28] angular speed and linear speed problems
27. Determine the angular speed and linear speed if 8.2 revolutions are competed in 3 seconds
and the radius is 7 centimeters.
28. A car tire has a diameter of 20 inches. When you drive your car on the freeway, your tire
rotates at a rate of 60 revolutions per minute. Find the angular speed in radians per minute, and
the linear speed in inches per second. Round to nearest tenth.
<Answer Keys> -----------------------------------------------------------------------------------------------1
1. amplitude: 4 period: 4 frequency:
phase shift: 0 vertical shift: -5 midline: y = -5
4
1

2. amp: 1 per: 2 freq:
p.s.: 
v.s.: 0 midline: y = 0
2
2
3


3
and x 
and x 
3. per:  vertical asymptotes: x 
4. per:  VA: x 
4
4
4
4



and x 
5. per: 6
VA: x  3 and x  3
6. per:
VA: x 
6
3
2
 3
2


7.
8.
9. does not exist
10. does not exist
11.
12.
3
3
4
3
13. b  29.5, c  23.0 and C  50
14. B  79 , a  9.4, and c  13.6
15. A  40.5 , B  111.8 and C  27.7 16. A  70 , B  70 and c  20.5
17. 177.60
20. sin  =
21. sin  =
18. 159.05 19. B  71 , C  60 and c  13.8 : B  109 , C  22 and c  6.0
2√5
5
√3
2
22. sin  = −
,cos  =
√5
5
, csc  =
√5
2
, tan  =−√3 , csc  =
√6
3
, cos  =
23. 57.5 ft 24. 21.8
√3
3
, sec  = √5 , cot  = ½
2√3
3
, sec  = -2 , cot  = −
, tan  = −√2 ,csc  =
−√6
2
, cot  =
√3
3
−√2
2
25. 492.3 ft (x=1866.0 -1373.7) 26. Yes ( x 
12000
 61735 ft )
tan11
27. angular speed =17.2 radians/second, linear speed =120.2 cm/second
28. angular speed =377.0 radians/minute, linear speed =62.8 inches/second