1 / 17

4.1 Radian and Degree Measure

4.1 Radian and Degree Measure. Objective. To use degree and radian measure. 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. . Angles.

valentino
Download Presentation

4.1 Radian and Degree Measure

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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

More Related