Trigonometry Worksheet Page 5
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22Therefore, we have two conversion formulas:
1. To convert from degrees to radians, multiply the degree measure by
.
# "
# "
2. To convert from radians to degrees, multiply the radian measure by
.
Note: radian measure does not use the degree symbol °, and often, the fraction is reduced but the
is
left alone.
Example 5: Perform the following conversions.
1. Convert 100° into radians.
2. Convert
radians into degrees.
'
Solution:
1. We multiply 100 by
and reduce:
# "
'
100
=
.
# "
'
Therefore, 100° is equivalent to
radians.
# "
2. We multiply
by
and reduce:
'
# "
# "
∙
=
= 32°.
'
'
= 1. Therefore,
radians is equivalent to 32°.
Notice that
'
Some common angles can be quickly determined. These are very common and should be committed to
memory:
180° =
Half circle (straight angle):
radians.
90° =
Quarter circle (right angle):
radians.
$
45° =
Eighth circle:
radians.
&
The four quadrants can be defined in both degree and radian measurement. Let
represent the value of
the angle.
Quadrant
Degree Range
Radian Range
0 <
<
1
0 <
< 90
$
<
<
2
90 <
< 180
$
%
<
<
3
180 <
< 270
$
%
<
< 2
4
270 <
< 360
$
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