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GBK Precalculus Jordan Johnson

GBK Precalculus Jordan Johnson. Today’s agenda. Greetings Intro Lesson: Angle Measure Classwork / Homework Clean-up. Important numbers. 0, 6, 4, 3, 2. Angles & Arc Length: Problem. Write a formula for the length of an arc, subtended by an angle of °, with radius r .

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GBK Precalculus Jordan Johnson

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  1. GBK PrecalculusJordan Johnson

  2. Today’s agenda • Greetings • Intro • Lesson: Angle Measure • Classwork / Homework • Clean-up

  3. Important numbers • 0, 6, 4, 3, 2.

  4. Angles & Arc Length: Problem • Write a formula for the length of an arc, subtended by an angle of °, with radius r.

  5. Angles & Arc Length: Answer • Write a formula for the length of an arc, subtended by an angle of °, with radius r.

  6. Problem: • Ugliness: • Extra factor of 1/360. • Formula requires a fraction. • Goal: Eliminate that fraction. • Historical trivia: • Division into 360° is believed to come from approximate year length. • Division of degrees into minutes/seconds is from Babylonian sexagesimal number system. • Proposed solution that never caught on: divide a right angle into 100 units called gradians (grad). • Still requires the fraction, though.

  7. Solution: Radian Measure • We’ll solve the problem by introducing a new way of measuring angles. • Objectives: • Measure angles in radian units. • Convert between degrees and radians. • Find trig function values of radians.

  8. Definition • The radian measure of an angle  is the ratio of an arc subtended by  to the arc’s radius. • Notice: a full circle is a 360° arc, so: • Radian measures are usually given in terms of .

  9. Alternate Definition • Equivalently, the radian measure of an angle  is the length of an arc on the unit circle subtended by ’s radii.

  10. Examples  Length of arc if r = 1 • /4 • /3 • 5 • 7 • /4 • /3 • 5 • 7

  11. Examples  Length of arc if r = 8 • /4 • /3 • 5 • 7 • (/4)8 = 8/4 = 2 • (/3)8 = 8/3 • 5  8 = 40 • 7  8 = 56

  12. Degrees  Radians • Converting from degrees to radians: • Given  in degrees, • Example: • Convert 80° to radians.Give both exact & approximate answers. • Answer: Exactly 4/9. (Approximately 1.3962634.)

  13. Radians  Degrees • Converting from radians to degrees: • Given  in radians, • Example: • Convert 12.5664 radians to degrees.Give approximate answer (to nearest integer). • Answer: About 720°. (Note that 12.5664  4.)

  14. Important numbers 0 6 4 3 2  0 /6 /4 /3 /2 Convert to degrees:  0° 30° 45° 60° 90°

  15. Homework • From Section 3-4: • Read pp. 110-115 and answer the Reading Analysis questions. • Do exercises Q1-Q10. • Do #1-3, 9, 11, 17, 21, 25, 29, 31, and 37-53 odd. • Due Tuesday, 11/2/2010.

  16. Clean-up / Reminders • Pick up all trash / items. • Push in chairs (at front and side tables). • See you tomorrow!

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