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What is the unit circle and how does it relate to the 6 trig functions?

What is the unit circle and how does it relate to the 6 trig functions?. What is the Unit Circle? What are coterminal angles? How do I convert degrees to radians and vice-versa? How do I use a paper plate to help me?. Vocabulary.

ericwallace
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What is the unit circle and how does it relate to the 6 trig functions?

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  1. What is the unit circle and how does it relate to the 6 trig functions? What is the Unit Circle? What are coterminal angles? How do I convert degrees to radians and vice-versa? How do I use a paper plate to help me?

  2. Vocabulary Initial side, terminal side, standard position, positive angle, negative angle, coterminal

  3. Two rays with the same endpoint make an angle.

  4. (This ray moves) Terminal Side The position after rotation. Initial Side The starting point. (This ray stays on the x-axis)

  5. Terminal Side Positive angle(counterclockwise) Negative angle(clockwise) Initial Side

  6. COTERMINAL ANGLES are two angles in Standard Position with the same terminal side. How could we find a coterminal angle for 60°?

  7. COTERMINAL ANGLES are two angles in Standard Position with the same terminal side. Add or Subtract 360° (or 2) to get Coterminal Angles

  8. There are infinitely many angles coterminal with your angle. You can rotate around the circle infinitely many times clockwise or counterclockwise and you still end up in the same spot.

  9. Ex. 1 Find two coterminal angles (one positive and one negative) for the given angle 750° or 30° a) 390° -330° more than one correct answer b) -120° 240° more than one correct answer -480°

  10. Ex. 2a Find two coterminal angles (one positive and one negative) for the given angle + 2 = 25/12 - 2 = -23/12 more than one correct answer

  11. Ex. 2b Find two coterminal angles (one positive and one negative) for the given angle + 2 = 8/3 - 2 = -4/3 more than one correct answer

  12. Ex. 3 Give the < measure represented by each rotation a) 5.5 rotations counterclockwise b) 3.3 rotations clockwise

  13. Convert From Degrees to Radians Convert From Radians to Degrees

  14. Convert from radians to degrees.

  15. Convert From Degrees to Radians Ex. 4 a) 135° b) 540° c) -270° 3

  16. Ex. 5 Convert From Radians to Degrees b) 2 a) -90 ° 114.59 °

  17. Convert From Degrees to Radians Ex. 6 144 -20 -/9 4/5

  18. With calculators it is convenient to use decimal degrees to denote fractional parts of degrees. Historically, however, fractional parts of degrees were expressed in minutes and seconds, using the prime (’) and double prime (”) notations, respectively.

  19. That is 1’ = one minute = 1/60 (1°) 1” = one second = 1/3600 (1°)

  20. Consequently, an angle of 64 degrees, 32 minutes, and 47 seconds is represented by the notation  = 64°32’ 47”

  21. Your calculator can convert to degrees, minutes and seconds using DMS. • Type in the decimal degrees → Angle (2nd + Apps) ↓ 4: DMS

  22. Express in degrees, minutes, seconds. 15.735° 7. 8. -213.842° 1544’6” -21350’31.2”

  23. You must convert degrees, minutes and seconds to decimal degrees using a formula.

  24. Express in degrees, minutes, seconds. 39°5’34” 9. 39+(5/60)+(34/3600)= 39.093 (rounded to thousandths place) -145°8’18” 10. -145.138 (not what you got? Why?)

  25. 14) 13) What quadrant are these angles in? 11) 107.9 12) 257.5 II III I IV

  26. Reference angles are the angle formed between the terminal side of an angle in standard position and the closest side of the x-axis. All reference angles measure between 0o and 90o.

  27. Reference Angle Rule: For any angle θ, 0°< θ<360°, its reference angle is defined by: Θ in Quadrant I 180° – Θ in Quadrant II

  28. Reference Angle Rule (cont.) Θ – 180° in Quadrant III 360° – Θ in Quadrant IV

  29. Ex. Determine the reference angle for each of the following positive angles. • 300o • b) 210o • c) 135o • d) 585o 60o 360-300 = 30o 210-180 = 180–135 = 45o 1st Find coterminal angle on unit circle 585-360=225 45o 225-180 =

  30. Ex. Determine the reference angle for each of the following negative angles. 1st You must find the POSITIVE coterminal angle on unit circle 45o • -45o • b) -425o • c) -120o • d) -330o -45o=315o 360-315= 65o -425o=295o 360-295 = -120o=240o 240–180 = 60o -330o=30o 30o

  31. What are your questions?

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