Math 129
Test 5
11/22/06
Name___________________________
This part must be done without a calculator. Show all work.
1.
2.
Sketch the angle. Find the exact value of the given angle. (e.g. cos 90 o = 0
 7 
cos 

 4 
ii) sin 
iv)
 3 
sin  
 2 
v)
)
(2 pts each)
 17 

 6 
 2 

 3 
i)
PART I _____/68
iii) cot 
  

 6 
tan 150
vi) sec 
The terminal side of an angle of t radians in standard position passes through the point
 4, 3 .
Find the exact value of:
(2 pts each)
i)
sin  t  = _______
ii)
cos  t  = _______
iii)
tan  t  = _______


3. Give the amplitude, period, & phase shift of y  3cos  2t 

 . Sketch the graph. Plot specific points. Label units.
4
(7 pts)
Amplitude _______
Period __________
Phase Shift ______
4. If cos t = -0.3 and  < t < 3/2, find
i)
5.
sin  t 
ii)
sin  2  t 
iii)
cos  t  3 
iv)


csc   t 
2 
v)
cot  t  3 
Find the exact value of the expression.


i) sin 1  sin
ii)
iii)
(3 pts each)
5 

6 

   
cos 1  cos 

 4 


 3 
sin cos 1   
 5 

(3 pts each)
6. Write as an algebraic expression in x.
(4 pts)
sec  arctan  5x   = _______________
7. Solve. Give answers in radians.
i) Find all solutions for
cos  x   sin  x   1
2
ii) Find all solutions for
tan3  x   3tan  x 
iii) Find all solutions on
2  x  2 for sin  x   1
(5 pts each)
Math 129
Test 5
11/22/06
Name___________________________
PART II ______/32
You may use a calculator on this part. If the calculator was used, write the expression that you keyed in. When recording final
answer give angles to two decimal places.
8. Solve the triangle if a = 15 and tan  A  
A = ________
5
. Use radian measure.
12
C = _________
B = __________
(6 pts)
C
a
c = ________
b
b = __________
B
c
A
9. An amateur radio operator erects a 75-foot vertical tower for an antenna. Find the angle of elevation to the top of the tower at a
point on level ground 50 feet from its base. Include a sketch. Use degree measure.
(7 pts)
10.
Ruth is flying a kite. Her hand is 3 feet above ground level, and is holding the end of a 215 ft long kite string which makes an
angle of 61o with the horizontal.
a)
Sketch a picture showing Ruth and the kite.
b) Find the height of the kite above ground.
(7 pts)
11. Prove the following identities.
(4 pts each)
a) 1  sin x  cos x  sin x cos x
4
2
2
b)
1
1

1
sin x  1 csc x  1
c)
1
 sec x tan x
csc x  sin x
2