1 13.2 radian and degree measure in this section, we will study the following topics: terminology...
TRANSCRIPT
1
13.2 Radian and Degree Measure
In this section, we will study the following topics:
Terminology used to describe angles Degree measure of an angle Radian measure of an angle Converting between radian and degree measure Find coterminal angles
3
13.2 Radian and Degree Measure
Standard Position
Vertex at origin
The initial side of an angle in standard position is always located on the positive x-axis.
4
13.2 Radian and Degree Measure
Positive and negative angles
When sketching angles, always use an arrow to show direction.
5
13.2 Radian and Degree Measure
Measuring Angles
The measure of an angle is determined by the amount of
rotation from the initial side to the terminal side.
There are two common ways to measure angles, in degrees
and in radians.
We’ll start with degrees, denoted by the symbol º.
One degree (1º) is equivalent to a rotation of of one
revolution.
1
360
7
Angles are often classified according to the quadrant
in which their terminal sides lie.
Ex1: Name the quadrant in which each angle lies.
50º
208º II I
-75º III IV
13.2 Radian and Degree Measure
Classifying Angles
Quadrant 1
Quadrant 3
Quadrant 4
8
13.2 Radian and Degree Measure
Classifying Angles
Standard position angles that have their terminal side
on one of the axes are called quadrantal angles.
For example, 0º, 90º, 180º, 270º, 360º, … are
quadrantal angles.
9
13.2 Radian and Degree Measure
Coterminal Angles
Angles that have the same initial and terminal sides are
coterminal.
Angles and are coterminal.
10
13.2 Radian and Degree Measure
Example of Finding Coterminal Angles
You can find an angle that is coterminal to a given angle by
adding or subtracting multiples of 360º.
Ex 2:
Find one positive and one negative angle that are
coterminal to 112º.
For a positive coterminal angle, add 360º : 112º + 360º = 472º
For a negative coterminal angle, subtract 360º: 112º - 360º = -248º
Ex 3. Find one positive and one negative angle that is coterminal with the angle = 30° in standard position.
Ex 4. Find one positive and one negative angle that is coterminal with the angle = 272 in standard position.
12
13.2 Radian and Degree Measure
Radian Measure
A second way to measure angles is in radians.
Definition of Radian:
One radian is the measure of a central angle that intercepts arc s equal in length to the radius r of the circle.
s
r
In general,
13
13.2 Radian and Degree Measure
Radian Measure
2 radians corresponds to 360
radians corresponds to 180
radians corresponds to 902
2 6.28
3.14
1.572
15
13.2 Radian and Degree Measure
Conversions Between Degrees and Radians
1. To convert degrees to radians, multiply degrees by
2. To convert radians to degrees, multiply radians by
180
180
Ex 7. Find one positive and one negative angle that is coterminal with the angle = in standard position.
Ex 8. Find one positive and one negative angle that is coterminal with the angle = in standard position.7
5
3
19
0°
360 °
30 °
45 °
60 °
330 °
315 °
300 °
120 °
135 °
150 °
240 °
225 °
210 °
180 °
90 °
270 °
Degree and Radian Form of “Special” Angles
0º 0 135º 270º
30º 150º 300º
45º 180º 315º
60º 210º 330º
90º 225º 360º
120º 240º
6
4
3
2
2
3
3
4
5
6
7
6
5
4
4
3
3
2
5
3
7
4
11
6
2
Common Degrees/Radians
Class Work
Convert from degrees to radians.1. 542. -300
Convert from radians to degrees.3.
4.
11
3
13
12