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Warm-Up:

Learn to convert degrees to radians and vice versa, solve coterminal angles, find intercepted arc lengths, record player angular and linear speeds, and calculate sector areas in this comprehensive warm-up lesson.

jodybrooks
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Warm-Up:

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  1. Warm-Up: If , find tan θ.

  2. 4.2 – Degrees & Radians Objectives: You should be able to convert degrees to radians & vice versa as well as use angle measures to solve real-world problems.

  3. Angles & TheirMeasures

  4. Radian Measure:

  5. Degree/Radian Conversions:

  6. Example 2:

  7. Coterminal Angles:

  8. Example 3: a. Identify all angles that are coterminal with 80°. Then find specifically one positive and one negative coterminal angle. b. Identify all angles that are coterminal with . Then find specifically one positive and one negative coterminal angle.

  9. Arc Length:

  10. Example 4: Find the length of the intercepted arc in a circle with a central angle measure and radius given. Round to nearest tenth if necessary a. Central angle: Radius: 4 in b. Central angle: 125° Radius: 7 cm

  11. Example 5: RECORDS A typical vinyl record has a diameter of 30 cm. When played on a turn table, the record spins at revolutions per minute. a. Find the angular speed, in radians per minute, of a record as it plays. Round to the nearest tenth.

  12. Example 5: RECORDS A typical vinyl record has a diameter of 30 cm. When played on a turn table, the record spins at revolutions per minute. b. Find the linear speed at the outer edge of the record as it spins, in centimeters per second.

  13. Area of a Sector:

  14. Example 6: Find the area of the sector of the circle. a. b.

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