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4.1

4.1. Demana, Waits, Foley, Kennedy. Angles and Their Measures. What you’ll learn about. The Problem of Angular Measure Degrees and Radians Circular Arc Length Angular and Linear Motion … and why Angles are the domain elements of the trigonometric functions. Why 360º ?.

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4.1

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  1. 4.1 Demana, Waits, Foley, Kennedy Angles and Their Measures

  2. What you’ll learn about • The Problem of Angular Measure • Degrees and Radians • Circular Arc Length • Angular and Linear Motion … and why Angles are the domain elements of the trigonometric functions.

  3. Why 360º? θ is a central angle intercepting a circular arc of length a. The measure can be in degrees (a circle measures 360º once around) or in radians, which measures the length of arc a.

  4. Navigation In navigation, the course or bearing of an object is sometimes given as the angle of the line of travel measured clockwise from due north.

  5. Radian A central angle of a circle has measure 1 radian if it intercepts an arc with the same length as the radius.

  6. Degree-Radian Conversion

  7. Example: Working with Degree and Radian Measure a. How many radians are in 135º? b. How many degrees are in radians? c. To stay healthy, Jess is tethered to a stake in the middle of her yard with rope. The rope measures 12 feet from the stake to her waist. If she travels for 50 degrees, how many feet did she travel (assume the rope is fully extended.

  8. Solution a. How many radians are in 135º?

  9. Solution Continued b. How many degrees are in radians?

  10. Solution Continued c. To stay healthy, Jess is tethered to a stake in the middle of her yard with rope. The rope measures 12 feet from the stake to her waist. If she travels for 50 degrees, how many feet did she travel (assume the rope is fully extended.

  11. Arc Length Formula (Radian Measure) WHY IS THIS THE FORMULA?????

  12. Arc Length Formula (Degree Measure) WHY IS THIS THE FORMULA?????

  13. Example: A Slice of Pizza

  14. Solution

  15. Solution

  16. Angular and Linear Motion

  17. Nautical Mile A nautical mile (naut mi) is the length of 1 minute of arc along Earth’s equator.

  18. Distance Conversions

  19. 4.1 Homework • HW: 17 - 24, 35-38, 45, 47, 55, 71, 72

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