P R E C AL C UL US H O NO R S T E ST R E VI E W
4.7 t o 4.8
Evaluate the expression wit h ou t a calculator.
1. arcsin
1
2
( )
2. arccos 0
2
2
3. tan −1 − 3
4. arcsin
5. tan −1 0
 1
6. cos −1  − 
 2
Evaluate the expression. Round your answer to two decimal places.
7. arcsin 0.4
8. cos −1 0.213
Find the exact value of the expression.
4

9. cos  arctan 

5

 5 
10. csc  arctan  −  
 12  

Write an algebraic expression that is equivalent to the expression.
1

11. cot  arctan 

x
12. sec arcsin (x − 1)

36 − x 2 
13. cos  arcsin

6


14. Your football landed at the edge of the roof of your school building. When you are 25
feet from the base of the building, the angle of elevation to your football field is 21°.
How high off the ground is your football?
15. A plane is 80 miles south and 95 miles east of Cleveland Hopkins International Airport.
What bearing should be taken to fly directly to the airport?
16. The sonar of a navy cruiser detects a submarine that is 4000 feet from the cruiser. The
angle between the water line and the submarine is 34°. How deep is the submarine?
17. A jet leaves Reno, Nevada and is headed toward Miami, Florida at a bearing of 100°.
The distance between the two cities is approximately 2472 miles.
a. How far north and how far west is Reno relative to Miami?
b. If the jet is to return directly to Reno from Miami, at what bearing should it
travel?
18. A plane is observed approaching your home and you assume that its speed is 550 miles
per hour. The angle of elevation of the plane is 16° at one time and 57° one minute later.
Approximate the altitude of the plane.
19. A ship leaves port at noon and heads due west at 25 knots. At 2 P.M. the ship changes
course to N 54° W. Find the ship’s bearing and distance from the port of departure at 3
P.M.
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