Geometry Semester 2
Homework on General Angles and Radians
1.
Name: _______________________________
y
θ is an angle in standard position, with
(3, –4) on its terminal side. Find:
a. sin 
θ
b. cos 
x
2.
c. tan 
d. cot 
e. sec 
f.
csc
( 3, –4)
Give two angles between –360o and 360o that are coterminal with each of these angles:
a. 480o
3.
4.
b. –750o
3
and 90    180 . Then the reference angle of θ is a special angle.
2
Sketch θ in standard position, and then give the exact values of:
Suppose cos   
a. sec 
b. sin 
c. tan 
d. 
Convert each degree measure to radians:
a. 30o
b. 150o
c. 60o
d. 300o
d. 180o
e. 270o
f. 360o
g. 75o
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5.
6.
7.
Convert each radian measure to degrees:
a.
3
4
b. 3
c.
5
3
e.

10
f.  2
g. 
3
5
d.
7
4
g.
5
12
Sketch each angle in standard position, and give the reference angle:
o
o
b. –55
a.
823
c.
92°
d. –170o
e.
5
radians
6
f.

3
radians
5
Find θ to the nearest tenth of a degree (and check your answers with your calculator) if:
a. sin   0.90631 and 90    180
b. cos  0.90631 and 270    360
c. tan   2.7475 and 180    270
d. sec  1.0642 and 180    270
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8.
9.
10.
a.
Use your calculator to find the value of sin 37o to 6 decimal places.
b.
Now use your calculator to find the value of sin–1(0.601815) to the nearest degree.
c.
Use your calculator to find the value of cos 137o to 6 decimal places.
d.
Now use your calculator to find the value of cos–1(–0.731354) to the nearest degree.
e.
Use your calculator to find the value of sin 137o to 6 decimal places.
f.
Now use your calculator to find the value of sin–1(0.681998) to the nearest degree.
Use your calculator to find the values of each to the nearest degree:
a.
sin–1(0.984808)
b. sin–1(–0.984808)
c.
cos–1(0.984808)
d. cos–1(–0.984808)
e.
sin–1(sin 55o)
f. tan–1(tan 75o)
g.
sin–1(sin 310o)
h. sin–1(sin –50o)
i.
cos–1(cos –50o)
j. tan–1(tan 200o)
For what values of θ is
a.
sin–1(sin θ) = θ?
c.
tan–1(tan θ) = θ?
b. cos–1(cos θ) = θ?
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11. Give the exact values of each of the following:
12.
a. sin 60 
b. sin( 60) 
c. cos(60) 
d. cos( 60) 
e. tan 60 
f. tan( 60) 
g. sin 150 
h. cos150 
i. sin 225 
j. cos 225 
k. tan 225 
l. tan 300 
m. sin 180 
n. cos180 
o. sin 270 
p. tan 315 
Give two values of θ between 0 and 360 degrees where possible:
a. sin  
1
2
b. cos 
c. tan   3
e. cos  
g. tan   1
1
2
d. sin   
1
2
f. sin   1
h. cos  1
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3
2
13.
14.
A circle has radius 10 cm. Find:
3
radians.
5
a.
the length of an arc intercepted by a central angle measuring
b.
the length of an arc intercepted by a central angle measuring 135o.
c.
the area of a sector intercepted by a central angle measuring
d.
the area of a sector intercepted by a central angle measuring 75o.
5
radians.
4
A bicycle wheel has a diameter of 26 inches. Someone is riding this bike.
a.
When a wheel rotates one revolution, through how many radians has it rotated?
b.
When each wheel has rotated one revolution, how far has the bike traveled?
c.
If the bike travels a distance of 10 feet, then through how many radians has each wheel
rotated?
d.
If the bike travels a distance of 10 feet, then how many rotations has each wheel made?
e.
How many times has each wheel rotated when the person has gone a distance of
680.68 feet?
f.
If each wheel is rotating at a rate of 100 times per minute, how fast is the person travelling
(Give the answer in miles per hour.)
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