# A surveyor determines that the angle of elevation of a mountain by pptfiles

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```									Math 129                  Test 5           11/21/07         Name___________________________                                  PART I _____/65
This part must be done without a calculator. Show all work.

1.      Sketch the angle. Find the exact value of the given function. (e.g. cos 90o = 0                )                               (2 pts each)

 7                                    3                                               17 
i)       cos                              ii) sin                                          iii) csc        
 6                                     4                                                 6 

 3                                                                                        10 
iv)      cot                              v)    tan  315                                  vi) sec         
 2                                                                                         3 

2.      The terminal side of an angle of t radians in standard position passes through the point            1, 5 .   Find the exact value of:
(2 pts each)
i)     sin  t  = _______                  ii)   cos t  = _______                           iii)   tan t  = _______

3. i) Give the amplitude, period, & phase shift of          y  2sin  3x    . Sketch the graph. Plot specific points. Label units.
(6 pts)

Amplitude _______

Period __________

ii) Sketch the graph of      y  tan  2x   3                                                         Phase Shift ______               (4 pts)

4. If sin t = -0.7 and 3  t  2 , find                                                                                               (2 pts each)
2

i)     cos t                                                          ii)   sin  2  t 

                                                                     
iii)     csc  t                                                      iv) tan     t
 2                                                                 2 

v)       cot t  10 

5.     Find the exact value of the expression.                                                                                           (2 pts each)

                                                                             7        
i) sin 1  sin                                                         ii)   arccos  cos            
        6                                                                      6         
         3  
iii)     tan  arcsin                                                 iv)    cos  arctan  2  
         4 

         9 
6. Write        sin  arctan    as an algebraic expression in x.
         x 
i) Find all solutions on    0  x  2 for 2sin  x   sin  x 
3

ii) Find all solutions for     2cos2  x   5cos  x   2
iii) Find all solutions on   0  x  4 for tan  x  (tan x  1)  0
 
3
Math 129            Test 5                   11/21/07         Name___________________________                PART II ______/35
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.
7
8. Solve the triangle if a = 6 and   csc  A      . Use radian measure.                                              (6 pts)
4
C
A = ________                  C = _________              B = __________

a               b
c = ________                  b = __________

B           c            A

9. An airplane leaves the runway climbing at 18o with an average speed of 275 feet per second for the first minute. Find the altitude
of the plane after one minute.                                                                                    (7 pts)

10. While traveling across flat land, you notice a mountain directly in front of you. The angle of elevation to the peak is 2.5 o. After
you drive 17 miles closer to the mountain, the angle of elevation to the peak is 9 o. Approximate the height of the mountain.
Include a labeled sketch in your solution.                                                                         (7 pts)

11. Prove the following identities.                                                                                       (5 pts each)
a) (cot x  csc x)(cot x  csc x )  1

cos  t 
b)                     sec t  tan t
1  sin  t 

cos x 1  sin x
c)                     2sec x
sin x  1 cos x

```
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