Name______

Exam 4

You must provide complete answers to the following questions. No credit will be given to correct answers without supporting work. Each question is worth 4 points. You may use your class notes, class textbook, and instructor. No other sources are permitted. This exam is due at the start of the final exam (Thursday, May 5, 2005 from 4:00P – 6:00P in 8-119). Good luck.

1. Find the exact value of .

2. Write as an algebraic expression in x free of trigonometric or inverse trigonometric functions.

3. Solve .

4. Solve .

5. Solve for all real solutions.

6. Solve the triangle with .

7. Solve the triangle with .

8. Two lookout posts, A and B, which are located 12.4 mi apart, are established along a coast to watch for illegal foreign fishing boats coming within the 3 mi limit. If post A reports a ship S at angle , and post B reports the same ship at angle , how far is the ship from post A? How far is the ship from the shore (assuming the shore is along the line joining the two observation posts)?

9. Solve the triangle with .

10. Los Angeles and San Francisco are approximately 600 km apart. A pilot flying from Los Angeles to San Francisco finds that after she is 200 km from Los Angeles the plane is off course. How far is the plane from San Francisco at this time (to two significant digits)?

11. Find the area of the triangle with .

12. Find the area of the triangle with .

13. Two docks are directly opposite each other on a southward flowing river. A boat pilot wishes to go in a straight line from the east dock to the west dock in a ferryboat with a cruising speed of 8.0 knots. If the river’s current is 2.5 knots, what compass heading should be maintained while crossing the river? What is the actual speed of the boat relative to land?

14. Find the magnitude of the vector .

15. Form a unit vector u with the same direction as .

16. Do problem 48 on page 371 of your text.

17. Find the dot product .

18. Find the angle between the vectors to one decimal place.

19. Change to exact polar coordinates with and .

20. Change to rectangular form.