In The Coordinate Plane ANGLES In The Coordinate Plane
Endpoint Ray
Endpoint Ray
Terminal Side ANGLE Endpoint Initial Side
Terminal Side ANGLE Vertex Initial Side
An Angle In Standard Position Initial Side Vertex
The Measure of an Angle Describes the amount and direction of rotation required to get from the initial side to the terminal side.
Counterclockwise has a positive direction
Clockwise has a negative direction
An Angle in Standard Position Is said to lie in the quadrant in which its terminal side falls.
II I III IV
II I A Positive Angle In Quadrant I III IV
II I III IV
II I A Negative Angle In Quadrant I III IV
II I III IV
II I A Positive Angle In Quadrant II III IV
II I III IV
II I A Negative Angle In Quadrant III III IV
II I III IV
II I A Positive Angle In Quadrant IV III IV
How Do We Usually Measure Angles? Degrees
What Quadrant does this angle in? It’s Terminal side lies on the positive y-axis What Quadrant does this angle in? NO Quadrant
What Quadrant does this angle in? It’s Terminal side lies on the negative x-axis What Quadrant does this angle in? NO Quadrant
One rotation counterclockwise Known Fact One rotation counterclockwise or 1 rot counterclockwise = 360º
Example
1 rot counterclockwise = 360º Find the degree measure of the angle and draw the angle in standard position. rot degrees 1 1 rot Known Fact 1 rot counterclockwise = 360º
Positive 270° tells us counterclockwise rotation Find the degree measure of the angle and draw the angle in standard position. rot degrees 1 1 rot Positive 270° tells us counterclockwise rotation
Next Example
Find the degree measure of the angle and draw the angle in standard position.
Known Fact One rotation clockwise
Next Example
rot degrees 1 1 rot Known Fact 1 rot clockwise = –360º Find the degree measure of the angle and draw the angle in standard position. rot degrees 1 1 rot Known Fact 1 rot clockwise = –360º
Negative 180° indicates a clockwise rotation Find the degree measure of the angle and draw the angle in standard position. rot degrees 1 1 rot Negative 180° indicates a clockwise rotation
Next Example
1 rot counterclockwise = 360º Find the degree measure of the angle and draw the angle in standard position. rot degrees 1 1 rot Known Fact 1 rot counterclockwise = 360º
Positive 840° tells us counterclockwise rotation Find the degree measure of the angle and draw the angle in standard position. rot degrees 1 1 rot Positive 840° tells us counterclockwise rotation
Protractor
Next Example
rot degrees 1 1 rot Known Fact 1 rot clockwise = – 360º Find the degree measure of the angle and draw the angle in standard position. rot degrees 1 1 rot Known Fact 1 rot clockwise = – 360º
How Do You Know What Quadrant?
How Do You Know What Quadrant?
How Do You Know What Quadrant? Protractor How Do You Know What Quadrant?
You Try
Find the degree measure of the angle for each rotation. Draw the angle in standard position. State which quadrant or axis on which the terminal side of each angle lies
Terminal side lies in the 2nd Quadrant – 2250 Terminal side lies in the 2nd Quadrant
Terminal side lies in the 3rd Quadrant 2160 Terminal side lies in the 3rd Quadrant
Terminal side lies in the 4th Quadrant 2800 Terminal side lies in the 4th Quadrant
Terminal side lies on the negative y-axis – 15300 Terminal side lies on the negative y-axis
Go The Other Way
1 rot counterclockwise = 360º 450° is how many rotations in which direction? Positive rotations 1 Known Fact 1 rot counterclockwise = 360º
1 rot counterclockwise = 360º 450° is how many rotations in which direction? ? rotations 1 Known Fact 1 rot counterclockwise = 360º
1 rot counterclockwise = 360º 450° is how many rotations in which direction? 1 rot rotations 1 Known Fact 1 rot counterclockwise = 360º
1 rot counterclockwise = 360º 450° is how many rotations in which direction? 1 rot rotations 1 Known Fact 1 rot counterclockwise = 360º
450° is how many rotations in which direction? 1 rot rotations 1 Counterclockwise
– 1530° is how many rotations in which direction? You Try
– 1530° is how many rotations in which direction? Clockwise