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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 S52E. Find the distance and bearing from the port to the ship at noon. (14 points)