Radians
RADIAN MEASURE
A radian is measure of angle. It is larger than a degree. Radian measure is widely used in Mathematics and
Physics. All trigonometry in Calculus is done in radians. One radian is the angle subtended by an arc of
length 1 in a circle of radius 1.

a
, when a  r , the angle subtended is one radian.
r
1 radian subtends an arc length of 1, 2 radians subtend an arc length of 2, and so on. In general,
subtend an arc length of  .
When the length is around the circle, this is the circumference c  2rr
Radian =
arclength 2r
=
= 2 .
r
radius


This is one revolution 2radians  360 .
or 
radians = 180 
Therefore

radians = 90 
2
1 radian =
180 


radians = 90 
2

radians = 45 
4

radians = 30 
6

radians = 60 
3
= 57.3
 radians
To convert from radians to degree, multiply by
e.g.
=
180 

.
4
 radians to degrees
3
4
180 
= 240.

3

To convert from degree to radians, multiply by
e.g. Convert 240  to radians

180 
240 
4
    radians .

3
180
Converting Between Radians and Degrees
1. Convert 270° to radians.
Since 180° equates to π, then:
The equivalent angle is
2. Convert
radians to degrees.
The equivalent angle is 30°
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3. Find the angle between 0 radians and 2π radians that corresponds to
I need to figure out how many cycles of 2π fit in
:
So I see that there are seven times of "one around", with
The corresponding angle is
left over.
radians.
4. Find the angle between 0 radians and 2π radians that corresponds to
This one works just like the previous one, but in radians. So I'll work in terms of
in terms of 360°.
The corresponding angle is
radians.
http://www.mathsisfun.com/algebra/trig-interactive-unit-circle.html
http://www.purplemath.com/modules/radians2.htm
EXIT CARD.
WHAT DID I LEARN TODAY?
2π radians, instead of
ASSESSMENT FOR YOUR LEARNING
____
1. Convert 135 to radians.
a.
c.
b.
____
d.
2. Which of the following radian measures is the largest?
a.
c.
d. 
b.
____
3. Starting on the positive x-axis and moving
one travel?
a. 3.14 m
b. 360 m
of the way around a circle that has radius 3 m, how far would
c. 6.28 m
d. 0.69 m
____
4. What is the arc length if the central angle is 225 and the radius of a circle is 3 cm?
a. 0.4166 cm
c. 2.4 cm
b. 2.25 cm
d. 3.75 cm
____
5. If the central angle is
radians, what should the radius of a circle be to make the arc length 1 m?
a. 0.424 m
b. 0.238 m
c. 2.356 m
d. 4.188 m
____
6. If a man walks around a circle 2.125 times, how many metres did he walk if the radius of the circle is 4 m?
a. 50.265 m
c. 53.407 m
b. 25.525 m
d. 47.123 m
____
7. If a ball travels around a circle of radius 4 m in 1.5 minutes, what is the angular speed of the ball?
a.
c.
radians/s
radians/s
b.
____
radians/s
8. Convert
9. If an object travels in a circle
a. 1052
b. 144
radians/s
radians to degrees.
a. 98.18
b. 330
____
d.
c. 300
d. 98.6
radians, at what degree measure is it, relative to where it started?
c. 72
d. 60
____ 10. If the radius of a pizza is 20 cm, what is the central angle in degrees that gives one person 30 cm of crust?
a. 120
c. 43
b. 35
d. 86
ASSESSMENT FOR YOUR LEARNING
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
A
B
C
D
B
C
A
B
C
D