The Radian
1
A radian compares the arc length of a circle to the radius of the circle
measure of an angle in =
radians
arc length
length of radius
1 rad means arc length is 1 and radius is 1
2
We have a classic formula that relates circumfrance and radius don't we?
C = 2πr
One complete rotation in degrees = _______
The arc length of one rotation is ________ which is called the _________
The radian measure of an angle of 360 is ________
one half of a rotation in degrees is ________
The arc length of one half a rotation is _________
The radian measure of 180 is _________
3
Ex #1
Complete the chart
Degrees
360
180
90
60
45
30
1
Radians
ARE you stuck?
In order to go from Degrees to Radians multipy by π
180
Convert 270 degrees to radians leave answer in terms of pi
Convert 315 degrees to radians leave answer in terms of pi
Convert 70 degrees to radians to the nearest tenth
Convert 205 degrees to radians to the nearest tenth
4
What about the reverse process?
To convert from Radians to Degrees multiply by
Convert Convert
180
π
to degrees
to degrees
Convert 1.57 radians to degrees
Convert ­1.4 radians to degrees
5
Ex #3
Use a calculator in radian mode to to find a decimal approximation for
Use a calculator in radian mode to to find a decimal approximation for
(did we catch the trick?)
Use a calculator in radian mode to to find a decimal approximation for cos 45
6
Example #4
Draw the angle in standard position
State the principal angle
Find one postive and one negative coterminal angle
7
Ex #6
Draw the angle in standard position
State the principal angle
Find one postive and one negative coterminal angle
8
Ex#7
Find the reference angle for the following rotation angles
a) b) c) 9
Homework
Pages 243 ­ 246 #1­11
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