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Trigonometry
Name ________________________________
Unit 1 Test Review
Date ______________________
Read each question carefully. Show your work for full credit. Leave all answers in exact form,
unless otherwise indicated.
1.
Which quadrant has positive x-values and negative y-values?
___________________
2.
What is the radius of the Unit Circle?
___________________
3.
What is the circumference of the Unit Circle?
___________________
4.
Sketch the angle  
2
. Then find sin(  ), cos( ), and tan(  ) for the angle.
3
sin(  ) = _____________ 

cos( ) = ______________

tan(  ) = _____________


5.
Sketch the 
angle  
11
. Then find sin(  ), cos( ), and tan(  ) for the angle.
6

sin(  ) = _____________


cos( ) = ______________
tan(  ) = _____________



Convert from degrees to radians or radians to degrees. Show your work.
6.
-125° = ______________
7.
4
= ________________
45

Coterminal Angles
8.
Find two coterminal angles (one positive and one negative) of


. _________ , _________
3
Evaluate each of the following:
9.
 12.
 15.
 
sin   = ______
4 
10.
5 
tan  = ______
 6 
11.
7 
sin   = ______
 2 
 13.
 
sec  = ______
3 
 14.
5 
cot  = ______
 4 
2 
csc
 = ______
 3 
 16.
sec2  = ______
 17.
9 
cos
 = ______
 2 
 18.
 

4cos603tan   = ______________
 4 
 20.

The point (3,5) is on the terminal side of an angle  in standard position.
Find the exact value of all six trigonometric function values for the angle  .
19.
sin  = ___________

cos = ___________

tan  = ___________

csc = ___________

sec = ___________

cot = ___________

 
cos  = ______
3 
tan  sin
3
= ___________
2


Arc Length, Area of a Sector, Angular Speed and Linear Speed
21.

Find the length of an arc on a circle with a radius of 5 meters intercepted by a central angle
4
of
radians.
3
22.
Find the area of the sector of a circle with a central angle of 3.4 radians and a radius of 5.2
inches.
23.
A sprinkler can water a lawn up to a distance of 50 feet. It turns through an angle of 120°.
Find the area of the lawn that can be watered by this sprinkler.
24.
A wheel has a diameter of 100 cm. If the wheel is supporting a craft moving at 45 kilometers
per hour, then what is the angular velocity of the wheel, to the nearest whole number of
revolutions per minute.
25.
A bicycle wheel has a diameter of 78 cm. If the wheel revolves at a rate of 120 revolutions per
minute, what is the linear velocity of the bike, in kilometers per hour? Round your answer to
the nearest tenth.
26.
Assume that the Earth’s orbit is circular, with a radius of 93,000,000 miles, and let “one year”
equal 365.25 days. Under these conditions, find the linear velocity of the Earth in miles per
second. Round to the nearest whole number of miles.
27.
A train is travelling at the rate of 10 mph on a curve of radius 2000 feet. Through what angle
will the train turn in one minute? Round to the nearest whole number of degrees.