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3.1 Radian Measure

3.1 Radian Measure. Objectives: Radian measure. Converting between Degrees and Radians. Finding Function Values for Angles in Radians. Page 83. Since a radian is defined as a ratio of two lengths, the units cancel and the measure is considered unit-less.

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3.1 Radian Measure

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  1. 3.1 Radian Measure Objectives: Radian measure. Converting between Degrees and Radians. Finding Function Values for Angles in Radians. Page 83

  2. Since a radian is defined as a ratio of two lengths, the units cancel and the measure is considered unit-less. • Therefore, if an angle measure is written with no degree symbol, it is assumed to be in radians. • Though it is not essential, it is often customary to write radians or rads after an input measured in radians, especially when doing conversions and canceling units.

  3. In many applications of trigonometry, radian measure is preferred over degree measure because it simplifies calculation and allows us to use the set of real numbers as the domain of the trig functions rather than just angles.

  4. Converting Standard Angles Between Degrees and Radians

  5. Example 1:

  6. Example 2

  7. You should memorize the following diagram.

  8. You should memorize the following table.

  9. Homework Assignment on the Internet Section 3.1(Read): Pp 107-109: 1-4all, 6,8,12,14,22-38even, 46, 48, 52, 58, 62, 66, 68,74,75.

  10. 3.2 Application of Radian Measure Objectives: Arc Length of a Circle. Sector of a Circle. Page 109

  11. Arc Length • The length (s) of the arc intercepted on a circle of radius (r) by a central angle θ (measured in radians) is given by the product of the radius and the angle, i.e., • s = r·θ. • Caution: θ must be in radians to use this formula.

  12. Example 1 • Find the length of the arc intercepted by a central angle θ = 135oin a circle of radius r = 71.9 cm.

  13. Example 2 • Find the distance in kilometers between Farmersville, California, 36° N, and Penticton, British Columbia, 49° N, assuming they lie on the same north-south line. The radius of the earth is 6400 km.

  14. Example 3 • A small gear and a large gear are meshed. An 80.0° rotation of the smaller gear causes the larger gear to rotate 50.0 . Find the radius of the larger gear if the smaller gear has a radius of 11.7 cm.

  15. Area of a Sector of a Circle A sector of a circle is the portion of the interior of the circle intercepted by a central angle.

  16. Example 4

  17. Example 5 • The Ford Model A, built from 1928 to 1931, had a single windshield wiper on the driver’s side. The total arm and blade was 10 inches long and rotated back and forth through an angle of 95°. If the wiper blade was 7 inches, how many square inches of the windshield did the blade clean?

  18. Homework Assignment on the Internet Section 3.2(Read): Pp 113-117: 2-6even, 10, 12, 16, 20, 24, 26, 28, 36, 38, 40, 44-50 even.

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