Download Chapter 4 Review

Chapter 4 Review
Pre-Calc/Trig
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Date____________________Period______
Reciprocal Identities:
Quotient Identities:
sin  =
csc  =
tan  =
cos  =
sec  =
cot  =
tan  =
cot  =
Pythagorean Identities:
1.
2.
3.
1. Find the complement and the supplement of each angle if possible.
a)
38
b)
2
5
2. Find one positive and one negative coterminal angle for each.
a)

4
7
b)
430
3. Sketch the angle in standard position and state the quadrant.
a)
4. Convert

5
8
5
to degrees.
9
5. Convert 265o to radians.
b)
7
4
Convert 
3
to degrees.
8
Convert ‒135o to radians.
6. Evaluate each of the six trigonometric functions for the given angle. (no decimals)
a)

5
4
b)
  120
sin  
sin  
cos 
cos 
tan  
tan  
csc 
csc 
sec 
sec 
cot  
cot  
7. Find the exact value of the six trigonometric functions of the angle θ given in the figure.
sin  
34
cos 
16
θ
tan  
csc 
sec 
cot  
8. Use the given function value to find the other five trigonometric functions. sec  
34
3
sin  
cos 
tan  
csc 
cot  
9. A circle has a radius of 10 inches. Find the length of the intercepted arc by a central angel of 150 .
10. In a circle, find the central angle (in radians) if the radius is 18 cm and the arc length is 4 cm.
11. Let (5, ‒4) be a point on the terminal side of θ. Find the values of the sin θ, cos θ, and tan θ.
12. If sin   
1
and cos  0 , find the values of the 6 trig functions.
4
13. Find the values of the reference angles for each of the following angles.
a.   127o
b.   525o
c.  
6
5
d.   
7
9
14. Evaluate the following.
 4 
a. csc 

 3 
 11 
b. cos 

 6 
 3 
c. tan   
 4 
d. sin  3 
 7 
e. cot 

 6 
 7 
f. sec  

 4 
1
15. a. If sin t  then sin(t ) 
3
b. If cos t  
4
then cos( t ) 
7
16. Name the quadrant:
a. cos  0 and tan   0
a. sin   0 and cot   0
a. sec  0 and tan   0
17. Find the interval for each.
a. y  2sin  2 x    1
b. y  3cos 5 x  4
x
y

3
tan
2
c.
4


y


cot
3
x



d.
4

18. Find the period of each.
a. y  sec  2 x     1
b. y  3cos x  4
x
c. y   tan 6  2


d. y   csc  5 x  3 
Graph each of the following. Identify any information indicated and graph each function.
19. y  sec 4 x  2
reciprocal function ____________________
amplitude ___________ period _______________
increment ____________ interval ___________
1


20. y   csc  x  
3
4

reciprocal function ________________
amplitude ___________ period _______________
21. y  4 tan
increment ____________ interval ___________
1
x
2
period ____________
asymptotes _______________________
x-intercepts ________________
asymptotes _______________________
x-intercepts ________________
1
22. y  cot 4 x
2
period ____________
23. Evaluate each of the following:
 3

 2 
 1

 2
a. arcsin  

3

3 


4 

3 
b. arccos 
c. arctan  
d. arcsin  sin 

 1 
e. cos  arcsin    
 2 

f. arcsin  cos

 1 
h. tan  arc cos    
 7 


 2 
i. cot  arcsin    
 5 



 5  

 4 
24. Solve the right triangle:
a.
18 inches
37o
b.
27 ft
4 ft

25. A guy wire runs from the ground to the top of a 45 foot telephone pole. The angle formed between
the wire and the ground is 32o. How far from the base of the pole is the wire attached to the ground?
26. A 25-foot ladder makes an angle of 48º with the ground as it leans against a wall. How far up the
wall does the ladder reach?
27. The height of a radio transmission tower is 90 meters, and it casts a shadow of length 45 meters. Find
the angle of elevation the sun.
28. An observer in a lighthouse 350 feet above the sea level observes two ships directly offshore. The
angles of depression to the ships are 4o and 6.5o. How far apart are the ships?
29. A passenger in an airplane at an altitude of 12 kilometers sees two towsn directly to the west of the
plane. The angles of depression to the towns are 32o and 57o. How far apart are the towns?
30. A ship leaves port at 10AM and heads due east at 20 knots, or 20 nautical miles per hour. At
11:30AM, the ship changes course to S 48o E. Find the ship’s bearing and distance from the port of
departure at 1:30 P.M .