Name ______________________
Date ____________Period _____
Precalculus Honors/GT
Review Test #4
I. Find the following:
__________ 1.
__________ 2.
__________ 3.
___________ 4.
5.
13
rotations (clockwise).
5
A gear rotates at a rate of 8 rotations per minute. Through how many degrees does it
rotate in 2 minutes and 12 seconds?
Find the degree measure for
Name two coterminal angles (one positive and one negative) for
5
(put answers in radians)
3
Change 1544616 to radians. Round your answer to three decimal places.
Express each angle measure in degrees:
9
a)
_________
b) 7.2 _________
4
__________ 6.
Express 107.435 in terms of degrees-minutes-seconds.
__________ 7.
Identify the angles between 0° and 400° whose terminal sides are on the line x = 0.
II. Find the arc length or area indicated:
__________ 8.
Determine the arc length of a circle with a diameter 8cm and a central angle
intercepting the arc of 135°. (Round to 3 decimal places)
__________ 9.
Determine the area of a sector of a circle with a radius of 2.5 in and a central angle
of 150°.
__________ 10.
A sprinkler on a golf course fairway is set to spray water over a distance of 85 feet
and rotates through an angle of 125°; find the area of the fairway watered by the
sprinkler.
III. Angular and Linear Velocities:
__________ 11.
Find the angular velocity in radians per second of a gear turning at 23.5
revolutions per minute.
__________ 12.
The minute hand of a watch is 12.5 cm long. What is the linear velocity of the tip of
this hand of the watch in cm per seconds?
__________ 13.
Determine the linear velocity of a point rotating at an angular velocity of 2.5 rad/sec
whose distance from the axis of rotation is 6.1 cm.
IV.
14.
Find each of the following:
Determine the quadrant in which each angle lies:
a) -260°
15.
___________
b)
11
4
________
c) 14.135
_________
Find the complement and supplement (if it exists) of each angle below:
a) 64°
complement ________
b)
7
4
supplement _________
complement __________
supplement __________
Find the following: (No Decimal Answers)
16.
The terminal side of an angle θ in standard position passes through the point (-4,8).
Find the exact values of :
a) cos θ = ________
17.
c) tan θ = ________
Find the exact values of the trig functions for θ if given: csc θ = 
a) sin θ = ________
18.
b) csc θ = ________
b) cot θ = ________
9
and cos θ < 0
5
c) sec θ = _______
Find  given the function below and 0    360 . (Two solutions)
1
3
a) cos θ = 
b) cot   
c) sec  2
2
3
______ _______
_____ ______
_____ ______
Find the following: (No Decimal Answers)
19.
Find the special angle trig values: (exact values)
a) cot 60 = _________
d) csc
20.

4
= _________
b) sin

6
= ________
e) cos30 = ______
Find the reference angle for each angle below:
5
a)
= _______
b)
-150° = _____
3
c) sec 45 = _______
f) tan
c)

3
= _______
334° = ______
21.
Find the quadrant(s) that satisfies the conditions below:
a) cos θ < 0 and tan θ < 0
b)
____________
22.
23.
___________________
Find the trig values. Round to 4 places.
2
= ___________
5
a)
sin (-347°) = ___________
b)
cot
c)
sec
11
= ___________
8
d)
tan  423317 = __________
Find the trig values below: (exact values)
a) cos
3
= _________
4
c) sin  240 = _________
e) sec
7
= ___________
6
b) tan 330 = _________
d) cot 3 = __________
f) csc  450 = ________
 7 
g) sin 
 = _________
 2 
h) tan 2 = __________
5
= ___________
3
j) csc 150 = ________
i) sec
24.
csc θ < 0
The Eiffel Tower in Paris casts a shadow 160 meters long when the angle of elevation to the sun is
6826 . Find the height of the tower.
__________________
25.
From the fire tower in Flatlands National Park, a forest ranger sighted a fire. The ranger
approximated the angle of depression to the fire to be 25° from his observation tower that was 38
meters above the ground. How far away from the base of the tower was the fire?
________________
26.
A pilot of a small plane was flying over an oil spill at an altitude of 10,000 feet. He found that the
near edge of the spill had an angle of depression of 58˚ and the far edge of the spill had an angle of
depression of 44˚. What is the width of the spill?