Angles and Their Measure Degrees
Math Analysis - Angles and Their Measure Degrees
An angle of rotation can be any size and rotate in any direction.
Standard position on the coordinate plane: An angle in standard position ...
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.
2. Has the initial ray or side along the positive horizontal axis.
1. Has a vertex at the origin.
vertex
Initial Ray
1
Math Analysis - Angles and Their Measure Degrees
3. Is rotating either clockwise or counter clockwise. Counterclockwise - positive Clockwise - negative
Draw an angle in standard position with a measure of
The most common angular measure is the degree, which is equivalent to 1/360 of a full rotation (counterclockwise) about the vertex.
Draw an angle in standard position with a measure of
2
Math Analysis - Angles and Their Measure Degrees
Draw an angle in standard position with a measure of
Draw an angle in standard position with a measure of
Draw an angle in standard position with a measure of
Draw an angle in standard position with a measure of
3
Math Analysis - Angles and Their Measure Degrees
Draw an angle in standard position with a measure of
Draw an angle in standard position with a measure of
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 =
4
Math Analysis - Angles and Their Measure Degrees
Converting from one measure to the other: Degrees to Radians
Radians to Degrees
multiply by
multiply by
Write each degree measure in radians.
120
-45 300
Write each radian in degree.
Angles are co-terminal if and only if their degree measures are different by multiples of 360 degrees. Example:
and
5
Math Analysis - Angles and Their Measure Degrees
Angles are co-terminal if and only if their degree measures are different by multiples of 360 degrees. Example:
Find the positive and negative co-terminal angles when
and
Find the positive and negative co-terminal angles when
Find the positive and negative co-terminal angles when
6
Math Analysis - Angles and Their Measure Degrees
7
An angle of rotation can be any size and rotate in any direction.
Standard position on the coordinate plane: An angle in standard position ...
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.
2. Has the initial ray or side along the positive horizontal axis.
1. Has a vertex at the origin.
vertex
Initial Ray
1
Math Analysis - Angles and Their Measure Degrees
3. Is rotating either clockwise or counter clockwise. Counterclockwise - positive Clockwise - negative
Draw an angle in standard position with a measure of
The most common angular measure is the degree, which is equivalent to 1/360 of a full rotation (counterclockwise) about the vertex.
Draw an angle in standard position with a measure of
2
Math Analysis - Angles and Their Measure Degrees
Draw an angle in standard position with a measure of
Draw an angle in standard position with a measure of
Draw an angle in standard position with a measure of
Draw an angle in standard position with a measure of
3
Math Analysis - Angles and Their Measure Degrees
Draw an angle in standard position with a measure of
Draw an angle in standard position with a measure of
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 =
4
Math Analysis - Angles and Their Measure Degrees
Converting from one measure to the other: Degrees to Radians
Radians to Degrees
multiply by
multiply by
Write each degree measure in radians.
120
-45 300
Write each radian in degree.
Angles are co-terminal if and only if their degree measures are different by multiples of 360 degrees. Example:
and
5
Math Analysis - Angles and Their Measure Degrees
Angles are co-terminal if and only if their degree measures are different by multiples of 360 degrees. Example:
Find the positive and negative co-terminal angles when
and
Find the positive and negative co-terminal angles when
Find the positive and negative co-terminal angles when
6
Math Analysis - Angles and Their Measure Degrees
7
