3.2 Radian and Degree Measure Notes
PART ONE:
Name: ___________________
Radians and Degrees
Angle in Standard Position:
Types of Angles:
θ
There are 360 degrees in ONE revolution.
Example 1:
Sketch the following angles in standard position.
a. 245°
b.
−170°
__________
__________
__________
__________
__________
__________
__________
__________
Radian Measure:
One radian is the measure of a central angle that intercepts an arc equal to the radius of the circle.
Draw in an angle with measure of “about” one radian.
Approximately how many radians are in a circle?
EXACTLY how many radians are in a circle?
≈ ____________ radians
= ____________ radians
2 rads
r
1 radian
r
What is circumference of a circle?
C = _______________
r
3 rads
r
6 rads
This means that one revolution is equal to _________ radians.
r
r
4 rads
r
5 rads
Example2:
a.
b. −
15π
4
Example 3:
a.
Sketch the following angles in standard position.
c. 4 rads
2π
3
State the quadrant or axis where each angle terminates.
157°
b.
e. −2π
f.
c.
−75°
5𝜋
252°
g. 3.75
3
Co-terminal Angles are angles that have the same initial and terminal sides.
Draw in three other angles co-terminal with the given angle.
How many angles are co-terminal with 120 ? ______________
Could you list of ALL of them? _________________________________
How many angles are co-terminal with
5𝜋
radians? ______________
4
Could you list of ALL of them? _____________________________________
d.
−390°
h. −5.12
Example 4:
State two coterminal angles for each given angle… one positive and one negative.
a.
40°
b.
−800°
5π
4
c.
d.
9π
e.
5
f.
−47°
PART TWO: Conversions Between Degrees and Radians
1 revolution is 2π radians
1 revolution is 2π radians
2π radians = 360°
360° = 2π radians
SO
1 radian = _______________ °
then
7 radians = _______________ °
SO
To convert rads ⇒ deg, multiply rads by
Example 1:
a.
135°
Example 2:
a.
−− π𝜋
2
2
180 °
𝜋
1° = __________________ radians
7° = __________________ radians
then
To convert deg ⇒ rads, multiply degrees by 𝜋 rads.
180
Convert from degrees to radians.
b.
5
540°
c.
−270°
c.
2
Convert from radians to degrees.
b.
9π
9𝜋
2 2