bell ringer (12-8-14) using any available source define: 1. radian 2. standard position 3....
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Bell Ringer (12-8-14)
Using any available source define:
1. Radian
2. Standard Position
3. Coterminal
4. Intercepted Arc
5. Reference Angle
6. Unit Circle
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Radians and the Unit Circle
Monday, December 8, 2014
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What is a radian?A radian is the measure of an angle determined by joining the center of a circle to the endpoints of an arc that is equal in length to the radius of the circle.
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How do we convert?
Since everything to do with circles is proportional…
angle in degrees = angle in radians 360 2π
Or…..
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Examples:Convert the following degrees to radians:
1. 225 2. 1403. 675
Convert the following radians to degrees:
4. π 5. 7π 6. π
4 2
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Unit Circle Info.A circle with a radius of 1 unit is called the Unit Circle.
In the unit circle, angles are measured from the x-axis. Positive angles are measured counterclockwise and negative angles are measured clockwise.
Angles in standard position are coterminal if they share the same terminal side.
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Examples:Find one angle with a positive measure and one angle with a negative measure coterminal with the given angle.
7. -35 8. -380 9. 645
10. 6π 11. - 3π12. 8π
5 2 7
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Central Angle and Intercepted Arc
When a central angle, , of a circle with radius r is measured in radians, then length of the intercepted arc, s, is given by the equation:
s = r
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Examples:13. r = 12m, = 3π
4
14.
15. Find the length of the intercepted arc if the radius is 3cm and the central angle is 60.
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Unit CircleFill in indicated degree and radian measure for the Unit Circle.
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Practice
Radians, Degrees, and Coterminal Angles
Classwork
Homework