1 / 14

13-3 Radian Measure ( p . 726)

13-3 Radian Measure ( p . 726). Algebra 2 Prentice Hall, 2007. Objectives… You will:. Content Recall geometric terms related to the parts of a circle and use them to convert degrees to radians and vice versa. Use the circumference formula to determine arc length. Language

galia
Download Presentation

13-3 Radian Measure ( p . 726)

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. 13-3 Radian Measure (p. 726) Algebra 2 Prentice Hall, 2007

  2. Objectives… You will: Content • Recall geometric terms related to the parts of a circle and use them to convert degrees to radians and vice versa. • Use the circumference formula to determine arc length. Language • Recognize when an angle’s measure is written in degrees or radians.

  3. Recall from Geometry… • A central angle of a circle is an angle with its vertex at the center of a circle. • An intercepted arc is the portion of the circle with endpoints on the sides of the central angle.

  4. Special Angle Measurements… • When a central angle intercepts an arc that has the same length as the radius of the circle, the measure of the angle is defined to be 1 radian.

  5. Special Angle Measurements… Because the circumference of a circle is 2r(and in a unit circle 1 radius = 1 radian), there are 2 radians in every circle. 360 degrees = 2 radians

  6. Think… • What do you see?

  7. Conversion Factors… Remember “unit analysis”… where you multiply by whatever fraction it takes to get rid of the old unit and turn it into the new one? ✕new unit /old unit --- cancel 1st top with 2nd bottom Ex. Convert 32 feet to inches.

  8. Conversion Factors… Degrees to radians multiply by π radians/180° Radians to degrees multiply by 180°/π radians

  9. Examples… Find the radian measure for each angle: 45 180 330 Find the degree measure for each angle: /3 radians 3/4 radians -2/3 radians NOW, find the radian measure for all the angles on your Unit Circle! HINT: start with the axes…

  10. Arc Length (with Degrees)… In Geometry, you found the length of an intercepted arc by multiplying the circumference by the fraction of the circle:

  11. Arc Length (and Radians)… When your angle is given in radians, simply multiply the radius by the radian measure: radians radius

  12. Your Turn… Ex. 4 Find the lengths of s and b:

  13. Real World Example Ex. 5A weather satellite in a circular orbit around Earth completes one orbit every 2 hours. The radius of Earth is about 6400 km, and the satellite orbits 2600 km above Earths’ surface. How far does the satellite travel in 1 hour?

  14. Assignment… • 13-3 p. 729: multof 3 (3-42, not 27); 47, 48, 74

More Related