Download PRECALCULUS TEST REVIEW 4.1 to 4.3 1. Consider the angle − 3

PRECALCULUS TEST REVIEW
4.1 to 4.3
4π
1. Consider the angle −
3
a. Sketch the angle in standard position.
b. Determine the quadrant in which the angle lies.
c. Determine one positive and one negative coterminal angles.
2. Consider the angle 280°.
a. Sketch the angle in standard position.
b. Determine the quadrant in which the angle lies.
c. Determine one positive and one negative coterminal angles.
Convert the angle measure from degrees to radians. If necessary, round your answer to three
decimal places.
3. −127.5°
4. 45o30′
Convert the angle measure from radians to degrees. If necessary, round your answer to three
decimal places.
5.
7π
6
6. −
2π
3
Evaluate the sine, cosine, and tangent of the angle without using a calculator.
7.
π
8. −
4
9. −210o
3π
4
10. 330o
Find the point (x, y) on the unit circle that corresponds to the real number t.
11. t =
5π
4
12. t = −
2π
3
Evaluate (if possible) the six trigonometric functions of the real number.
13. t =
5π
6
14. t = −
5π
3
Evaluate the trigonometric function using its period as an aid.
15. sin
7π
4
 19π 
16. cos  −
 6 
Use a calculator to evaluate the trigonometric function. Round your answer to four decimal
places.
17. tan130o
18. csc
3π
5
Use the given function value and trigonometric identities (including the cofunction identities) to
find the indicated trigonometric functions.
13
13
, secθ =
2
3
a. sinθ
19. cscθ =
b. cosθ
c. tanθ
d. sec(90°−θ)
Find the exact values of the six trigonometric functions of the angle θ shown in the figure.
20.
21.
6
θ
2
8
15
θ
22. Find the length of the arc on a circle with a radius of 10 inches intercepted by a central
angle of 145°.
23. The wheel of a machine rotates at the rate of 300 rpm (rotation per minute). If the
diameter of the wheel is 80 cm, what is the angular (in radian per second) and linear
speed (in cm per second) of a point on the wheel?
24. On the top of the Sears Building in Chicago, is a TV tower. From a point 300 ft. away
the bottom of the tower is at an angle of elevation equal to 42.14 degrees and the top of
the tower is at an angle of elevation equal to 45.81 degrees. How tall is the tower?
25. John wants to measure the height of a tree. He walks exactly 100 feet from the base of
the tree and looks up. The angle from the ground to the top of the tree is 33º. How tall is
the tree?
26. An airplane is flying at a height of 2 miles above the ground. The distance along the
ground from the airplane to the airport is 5 miles. What is the angle of depression from
the airplane to the airport?