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The Unit Circle

The Unit Circle. Chapter 3 Section 3. Unit circle circle with center at the origin and radius of 1 unit. radius 1 unit. r = 1 unit. y. y. x. x. Think: COFUNCTION THEOREM sin 30 = cos 60 c os 30 = sin 60. CIRCLE. UNIT. Use the unit circle to find: sin 30° = cos 45° =

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The Unit Circle

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  1. The Unit Circle Chapter 3 Section 3

  2. Unit circle circle with center at the origin and radius of 1 unit radius 1 unit r = 1 unit y y x x

  3. Think: COFUNCTION THEOREM sin 30 = cos 60 cos 30 = sin 60

  4. CIRCLE UNIT

  5. Use the unit circle to find: sin 30° = cos 45° = cos 240° = sin 90° = cos 270° =

  6. Use the unit circle to find: F. sec 330° = G. csc 270° = H. sec = I. csc = J. csc 180° =

  7. To find tangent and cotangent, use. . . RATIO IDENTITIES in the unit circle in the unit circle

  8. Use the unit circle to find: K. tan 30° = L. tan 150° = M. tan = N. cot = O. cot 90° = Most calculators won’t perform this operation, mistakenly giving an error message instead of zero!

  9. ALL S We can use the unit circle to find angles. Consider the problem In which quadrants is the sine negative? In those quadrants, where is sine = ? Given the constraints , then T C Recall: sine is y!

  10. Consider the problem In which quadrants is the sine positive? In those quadrants, where is sine = ? remember: radians! Given no other constraints , then

  11. Use the unit circle to find θ if: P. Q. R. S.

  12. On a graphing calculator: Parametric (FuncParPolSeq) Degree (Radian Degree) MODE x1T = cosT (x,T,θ,n) y1T = sin T (x,T,θ,n) y= Tmin = 0° Xmin = -1.5Ymin = -1.5 Tmax = 360° Xmax = 1.5 Ymax = 1.5 step = 15° Xscl = 1 Yscl = 1 WINDOW ZOOM Zoom Square TRACE Use for counterclockwise

  13. P(x,y)

  14. P(x,y) sine cosine

  15. P(x,y) line radius sine cosine

  16. P(x,y) line radius sine cosine

  17. P(x,y) line radius sine cosine

  18. P(x,y) line radius sine cosine

  19. P(x,y) line radius sine cosine

  20. P(x,y) tangent radius sine cosine

  21. cotangent P(x,y) tangent radius sine cosine

  22. cotangent P(x,y) tangent radius sine cosine line

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