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```130
Angela Hesse – Math 169 Independent Study: Final Examination
Fall 2012
Name:
Show your work. Correct answers with no support may not get full credit. Incorrect answers with no work will get no credit.
1. Find a formula of the form f ( x ) = Asin ( Bx + C ) such that A > 0, B > 0, and C has the
smallest positive value for the graph shown below. (8 points)
2. Solve each of the following equations. Give exact answers and a 3 decimal place
approximation when appropriate. (8 points each)
(a) 4.2 ln (3x +1) - 2.4 =13.56
(b) 2.6 (1.935) = 5.46 (1.075)
x
x
(c) 7.2 (1.45) - 5 = 23.8
x
3. Find the six trigonometric functions of the angle  for the right triangle shown. Give exact
values for each. (12 points)
73
48

4. If (-140, -51) is on the terminal side of an angle , list all six trigonometric values of .
Give exact values for each. (12 points)
5. Solve the right triangle having a = 7.2 and b = 12.4.
(12 points)
6. Solve the triangle (not necessarily right) having  = 36,  = 48, and a = 8.
7. Complete the table below, give exact values.

p
0
6
p
4
p
3
(10 points)
p
2
sin (q )
cos (q )
8. Give exact values for the following. Show your work.
91
(a) tan ( arcsin (- 109
))
(
(b) sin arccos
( ))
x
2
(8 points each)
(12 points)
9. A tree leans away from the sun at an angle of 9 from the vertical. The tree casts a shadow
20 meters in length when the angle of elevation of the sun is 62. Find the height of the tree.
(10 points)
10. A ship leaves port at 10am and travels due east at 22mph. At 11am it changes course to a
heading of S52E. Find the distance and bearing from the port to the ship at noon. (14 points)
```
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