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Radian Measure: A Pre-Calculus Adventure

Explore radian and degree measures, coterminal angles, conversions, and more in your Pre-Calculus journey. Calculate arc lengths, linear speed, angular speed, and more with practical examples and tips.

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Radian Measure: A Pre-Calculus Adventure

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  1. SFM Productions Presents: Another tremendous time to be had in your continuing Pre-Calculus experience! 4.1 Radian and Degree Measure

  2. Homework for section 4.1 p288 #17-113 eoo (skip 37)

  3. Angles Angles inStandard Position Terminal Terminal Initial Initial

  4. Positive and Negative angles Positive Negative

  5. Coterminal angles Angles that share the terminal side…

  6. Coterminal angles

  7. Radian Measure: One radian is the measure of a central angle:θ (theta) equal in length to the radius r of the circle. that intercepts an arc s If s = r,thenθis equal to 1 radian If s = 2r, thenθis equal to 2 radians s r If s = 3r, thenθis equal to 3 radians θ r

  8. Radian Measure… If s = r, thenθis equal to 1 radian. That means the ratio of s to r is equal to 1 radian.

  9. Radian Measure: What is the formula for the circumference of a circle? If s is the arc length of our angle in question, what is s equal to if the angle is a complete 360 degrees?

  10. Coterminal angles (using radians) Complementary angles add up to…… Supplementary angles add up to……

  11. How to convert from radians to degrees

  12. How to convert from degrees to radians

  13. How to convert from degrees to decimal degrees The easiest way is to useyour calculator…the book showsthe old hand calculation, butI’m sure you don’t care aboutthat, so I won’t waste our time…so, for now, break out BOB…

  14. θis always calculated using radians. A circle has a radius of 4 inches. What is the length of the arc intercepted by a central angle of 2400?

  15. Linear speed - along the circular arc of radius r. Angular speed - if θis in radians.

  16. The second hand on a clock is 10.2 cm long. What is the linear speed of the tip of the second hand? (hint: determine what 1 revolution gives you to work with)

  17. A small stone wheel with a 10 inch radius is rolling along the ground and makes 1.2 revolutions per second. a) find the angular speed of the wheel.b) find your speed if you are in front of the wheel and do not want to get hit.(hint: determine what 1 revolution gives you to work with)

  18. Go! Do!

  19. Pre-Cal

  20. How to convert from degrees to decimal degrees Degrees may be divided into smaller sub units called minutes and minutes may be divided into units called seconds. 360 degrees make 1 revolution (or 1 complete circle) 60 minutes make up 1 degree 60 seconds make up 1 minute Change to decimal degree…

  21. How to convert from decimal degrees to degrees

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