4.1 Radian and Degree Measure

1. 4.1 Radian and Degree Measure

2. Objective • To use degree and radian measure.

3. Angles • An angle is determined by rotating a ray about its endpoint. • The starting point of the ray is the initial side. • The ending position is the terminal side.

4. Angles • The endpoint of the ray is called the vertex of the angle. • An angle in standard position has its initial side on the positive x-axis and its vertex at the origin.

5. Angles • If the rotation of the ray is counterclockwise the angle has positive measure. • If the rotation of the ray is clockwise the angle has negative measure.

6. Angles • An angle in standard position is said to lie in the quadrant in which its terminal side lies. • A central angle of a circle is an angle whose vertex is on the center of the circle.

7. Degree Measure • An angle generated by one complete counterclockwise rotation measures 360°. • One generated by a complete clockwise rotation measures -360°.

8. Coterminal angles • Angles that have the same initial and terminal sides are called coterminal.

9. Radian Measure • The measure of an angle is determined by the amount of rotation from the initial side to the terminal side.

10. Definition of a Radian • One radian is the measure of a central angle θ that intercepts an arc s equal in length to the radius r of the circle. Algebraically this means that θ = s / r where θ is measured in radians. Radian Demo http://id.mind.net/~zona/mmts/trigonometryRealms/radianDemo1/RadianDemo1.html

11. The circumference of a circle is 2πr. There are 2πradians around the circumference of a circle. • There are about 6.28 radians in a full circle.

12. 1 radians = 57.29° • 1 degree = 0.017 radians

13. To convert degrees to radians: • To convert radians to degrees

14. When no units of angle measure are specified, radian measure is implied.

15. ExampleConverting from Degrees to Radians • 135° 3π/4 • 540° 3π • -270° -3π/2

16. ExampleConverting from Radians to Degrees