1 / 14

6.3 Angles & Radian Measure

6.3 Angles & Radian Measure. Objectives: Use a rotating Ray to extend the definition of angle measure to negative angles and angles greater than 180°. Define Radian Measure and convert angle measures between degrees and radians. Angles of Rotation.

trella
Download Presentation

6.3 Angles & Radian 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. 6.3 Angles & Radian Measure Objectives: Use a rotating Ray to extend the definition of angle measure to negative angles and angles greater than 180°. Define Radian Measure and convert angle measures between degrees and radians.

  2. Angles of Rotation Positive angles are rotated counter-clockwise & negative angles clockwise. Standard position has the initial side on the x-axis & the vertex on the origin.

  3. Radians & the Unit Circle Radians are used to measure angles using arc length. Circumference: r = 1 180° = π 0° = 360° = 2π

  4. Example #1Convert from Radians to Degrees

  5. Example #2Convert from Degrees to Radians 150° -330° 540°

  6. Example #3Find the angle measures from each graph. 360° - 60°= 300° -360° + 90° + 115° = -155° 5(180°) = 900°

  7. Example #4Draw the following angles in standard position. State the quadrant in which the terminal side is located. -110° 530°

  8. Example #4Draw the following angles in standard position. State the quadrant in which the terminal side is located. 3400°

  9. Example #4 (continued…)Draw the following angles in standard position. State the quadrant in which the terminal side is located.

  10. Arc Length of a Circle Depending on whether an angle is given in radians or degrees the formulas for arc length vary slightly, although the concept remains the same. For radians: For degrees: The key to learning this is not to memorize either formula, but to build on what you already know. The length of an arc is a fraction of the distance around the entire circle (circumference). Multiply that fraction by the circumference of the circle and you get the arc length.

  11. Sector Area of a Circle Depending on whether an angle is given in radians or degrees the formulas for sector area also vary. For radians: For degrees: And just like arc length, the formulas for sector area are based on the same concept:

  12. Example #5 Find the Arc Length & Sector Area of the following: A.

  13. Example #5 Find the Arc Length & Sector Area of the following: B.

  14. Example #6Arc Length The second hand on a clock is 5 inches long. How far does the tip of the hand move in 45 seconds? 12 11 1 10 2 5’’ 9 3 4 8 7 5 6

More Related