May 19, 2016
Topic: Angles and Radian Measure
Objective: To learn about radian measure.
Also:
* to graph angles in standard position
* know what coterminal angles are
* to convert between radian and degrees
Why: Angles in Precalculus and Calculus use radian measure more frequently
than degrees.
May 19, 2016
Obj: To learn about Radian Measure
Graphing Angles in Standard Position:
y
Standard Position:
initial side
vertex at origin, initial side on the positive
horizontal.
x
positive angles: terminal side moves
counterclockwise
negative angles: terminal side moves
clockwise
40o
-40o
y
initial side
x
y
initial side
x
May 19, 2016
Graph the following angles in standard position:
1. 210o
y
2. -330o
Obj: To learn about Radian Measure
y
x
3. 90o
y
x
4. -45o
x
y
x
May 19, 2016
Obj: To learn about Radian Measure
Coterminal Angles:
Angles with different measure but when graphed in standard position have
the the same terminal side.
Graph the following angles in standard position: 30o, -330o, 390o
y
x
How do you find a larger and smaller coterminal angle to a given angle?
Find one larger and one smaller coterminal angle to 120o.
May 19, 2016
Radian Measure:
Obj: To learn about Radian Measure
When a central angle intercepts an arc
that has the same length as the radius
of the circle, the measure of the angle is
defined to be 1 radian.
How many radians in one revolution?
What is the circumference of a circle?
y
x
May 19, 2016
Converting Degrees
r
d
=
2π
360o
Radians.
Obj: To learn about Radian Measure
May 19, 2016
Obj: To learn about Radian Measure
Convert each degree measure into radians.
Convert each radian measure into degrees.
1. 45o
1.
2. -60o
2.
5π
3
π
2
3. 210o
3.
5π
4
May 19, 2016
Obj: To learn about Radian Measure
Important Radian Measures:
30o
45o
60o
Other important radian measures:
y
900
180o
270o
360o
x
May 19, 2016
Obj: To learn about Radian Measure
May 19, 2016
Obj: To learn about Radian Measure
Place the following degree angle measures on the Unit Circle.
30
60
225
210
120
135
45
90
150
240
360
0
300
315
180
330
270
Then, convert each degree measure to radian measure and label on the Unit Circle.
May 19, 2016
Obj: To learn about Radian Measure
Place the following degree angle measures on the Unit Circle.
30
60
225
210
120
135
45
90
150
240
360
0
300
315
180
330
270
Then, convert each degree measure to radian measure and label on the Unit Circle.
May 19, 2016
Obj: To learn about Radian Measure
HF:
* Complete the Unit Circle with degrees and radians.
* Worksheet (Radians)