coterminal angles and radian measure
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Coterminal Angles and Radian Measure
11 April 2011
The Unit Circle – Introduction
Circle with radius of 1 1 Revolution = 360°
2 Revolutions = 720°
Positive angles move counterclockwise around the circle
Negative angles move clockwise around the circle
STAND UP!!!! Turn –180° (clockwise) Turn +180° (counterclockwise)
Turn +90° (counterclockwise) Turn –270° (clockwise)
What did you notice?
Coterminal Angles
co – terminal
Coterminal Angles – angles that end at the same spot
with, joint, or together
ending
Coterminal Angles, cont.
Each positive angle has a negative coterminal angle
Each negative angle has a positive coterminal angle
Coterminal Angles, cont.
70°
250°
–20°
–290°
Solving for Coterminal Angles
If the angle is positive, subtract
360° from the given angle.
If the angle is negative, add 360°
from the given angle.
Your Turn
Find a negative coterminal angle of the following:
Find a positive coterminal angle of the following:
110° 270° –30° –240°
45° 315° –180° –330°
Multiple Revolutions
Sometimes objects travel more than 360°
In those cases, we try to find a smaller, coterminal angle with which is easier to work
Multiple Revolutions, cont.
To find a positive coterminal angle,subtract 360° from the given angle until you end up with an angle less than 360°
75360435
435360795
Your Turn
For the following angles, find a positive coterminal angle that is less than 360°:
1. 570° 2. 960°
3. 1620° 4. 895°
Your Turn, cont.
5. 45° 6. 250° 7. –20°
8. 720° 9. –200°
Radian Measure
3.57180
radian
Another way of measuring angles Convenient because major measurements of a
circle (circumference, area, etc.) are involve pi Radians result in easier numbers to use
Radian Measure, cont.
Converting Between Degrees and Radians
To convert degrees to radians, multiply by
To convert radians to degrees, multiply by
180
180
Converting Between and Radians, cont
Degrees → Radians Radians → Degrees
2205
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