Angles of Rotation
Unit 2 - Circular Functions
(1) Angles and Their Measure Day 1
Angles of Rotation
An angle of rotation can be any size and rotate in any direction.
1
Unit 2 - Circular Functions
(1) Angles and Their Measure Day 1
The measure of rotation is given in relation to a fixed point.
When the rotation stops it ends at the terminal side of the angle.
Standard position on the coordinate plane: An angle in standard position ...
1. Has a vertex at the origin.
vertex
2
Unit 2 - Circular Functions
(1) Angles and Their Measure Day 1
2. Has the initial ray or side along the positive horizontal axis.
Initial Ray
3. Is rotating either clockwise or counter clockwise. Counterclockwise - positive Clockwise - negative
3
Unit 2 - Circular Functions
(1) Angles and Their Measure Day 1
Draw an angle in standard position with a measure of
Draw an angle in standard position with a measure of
4
Unit 2 - Circular Functions
(1) Angles and Their Measure Day 1
Draw an angle in standard position with a measure of
Draw an angle in standard position with a measure of
5
Unit 2 - Circular Functions
(1) Angles and Their Measure Day 1
Draw an angle in standard position with a measure of
Draw an angle in standard position with a measure of
6
Unit 2 - Circular Functions
(1) Angles and Their Measure Day 1
Draw an angle in standard position with a measure of
Draw an angle in standard position with a measure of
7
Unit 2 - Circular Functions
(1) Angles and Their Measure Day 1
A second common angular measure is radian. The measure in radians of a central angle of the circle is equal to the ratio of the length of the intercepted arc (s) to the radius (r) of the circle. 1 rotation =
8
Unit 2 - Circular Functions
(1) Angles and Their Measure Day 1
Use what you did in identifying angles in radian measure to sketch
Sketch
9
Unit 2 - Circular Functions
(1) Angles and Their Measure Day 1
Sketch
Sketch
10
Unit 2 - Circular Functions
(1) Angles and Their Measure Day 1
Sketch
Sketch
11
Unit 2 - Circular Functions
(1) Angles and Their Measure Day 1
Sketch
Sketch
12
Unit 2 - Circular Functions
(1) Angles and Their Measure Day 1
Sketch
Sketch
13
Unit 2 - Circular Functions
(1) Angles and Their Measure Day 1
Sketch
Converting from one measure to the other: Degrees to Radians
multiply by
Radians to Degrees
multiply by
14
Unit 2 - Circular Functions
(1) Angles and Their Measure Day 1
Write each degree measure in radians.
120
-45 300
Write each radian in degree.
15
(1) Angles and Their Measure Day 1
Angles of Rotation
An angle of rotation can be any size and rotate in any direction.
1
Unit 2 - Circular Functions
(1) Angles and Their Measure Day 1
The measure of rotation is given in relation to a fixed point.
When the rotation stops it ends at the terminal side of the angle.
Standard position on the coordinate plane: An angle in standard position ...
1. Has a vertex at the origin.
vertex
2
Unit 2 - Circular Functions
(1) Angles and Their Measure Day 1
2. Has the initial ray or side along the positive horizontal axis.
Initial Ray
3. Is rotating either clockwise or counter clockwise. Counterclockwise - positive Clockwise - negative
3
Unit 2 - Circular Functions
(1) Angles and Their Measure Day 1
Draw an angle in standard position with a measure of
Draw an angle in standard position with a measure of
4
Unit 2 - Circular Functions
(1) Angles and Their Measure Day 1
Draw an angle in standard position with a measure of
Draw an angle in standard position with a measure of
5
Unit 2 - Circular Functions
(1) Angles and Their Measure Day 1
Draw an angle in standard position with a measure of
Draw an angle in standard position with a measure of
6
Unit 2 - Circular Functions
(1) Angles and Their Measure Day 1
Draw an angle in standard position with a measure of
Draw an angle in standard position with a measure of
7
Unit 2 - Circular Functions
(1) Angles and Their Measure Day 1
A second common angular measure is radian. The measure in radians of a central angle of the circle is equal to the ratio of the length of the intercepted arc (s) to the radius (r) of the circle. 1 rotation =
8
Unit 2 - Circular Functions
(1) Angles and Their Measure Day 1
Use what you did in identifying angles in radian measure to sketch
Sketch
9
Unit 2 - Circular Functions
(1) Angles and Their Measure Day 1
Sketch
Sketch
10
Unit 2 - Circular Functions
(1) Angles and Their Measure Day 1
Sketch
Sketch
11
Unit 2 - Circular Functions
(1) Angles and Their Measure Day 1
Sketch
Sketch
12
Unit 2 - Circular Functions
(1) Angles and Their Measure Day 1
Sketch
Sketch
13
Unit 2 - Circular Functions
(1) Angles and Their Measure Day 1
Sketch
Converting from one measure to the other: Degrees to Radians
multiply by
Radians to Degrees
multiply by
14
Unit 2 - Circular Functions
(1) Angles and Their Measure Day 1
Write each degree measure in radians.
120
-45 300
Write each radian in degree.
15
