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Positive Angles

Positive Angles. Prepared by Title V Staff: Daniel Judge, Instructor Ken Saita, Program Specialist East Los Angeles College. Click one of the buttons below or press the enter key. BACK. NEXT. EXIT. © 2002 East Los Angeles College. All rights reserved.

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Positive Angles

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  1. Positive Angles Prepared by Title V Staff:Daniel Judge, InstructorKen Saita, Program SpecialistEast Los Angeles College Click one of the buttons below or press the enter key BACK NEXT EXIT © 2002 East Los Angeles College. All rights reserved.

  2. Generating a positive right angle . . . BACK NEXT EXIT

  3. Rotate the initial side counter-clockwise (¼ revolution). BACK NEXT EXIT

  4. Generating a positive straight angle . . . BACK NEXT EXIT

  5. Rotate the initial side counter-clockwise (½ revolution). BACK NEXT EXIT

  6. m(a) = 180 Why? BACK NEXT EXIT

  7. Rotate ¼ revolution ccw • Rotate another ¼ revolution ccw • You have rotated ½ revolution ccw! • 90 + 90 = 180 BACK NEXT EXIT

  8. Note: Any angle that measures 180 is called a straight angle. BACK NEXT EXIT

  9. Rotate the initial side counter-clockwise ¾ revolution. BACK NEXT EXIT

  10. So that, m(a) = 90 + 90 + 90 m(a) = 270 a INITIAL SIDE TERMINAL SIDE BACK NEXT EXIT

  11. Rotate the initial side counter-clockwise 1 revolution BACK NEXT EXIT

  12. So that, m(a) = 90 + 90 + 90 + 90 m(a) = 360 a Note: Initial side = terminal side. BACK NEXT EXIT

  13. Q: What would a 45 angle look like? Answer -- BACK NEXT EXIT

  14. Q: What would a 30 angle look like? Answer -- BACK NEXT EXIT

  15. Note BACK NEXT EXIT

  16. Q: What would a 120 angle look like? Answer -- TERMINAL SIDE TERMINAL SIDE INITIAL SIDE INITIAL SIDE BACK NEXT EXIT

  17. Note: this procedure can be used to generate the angles 120, 150, 180 210, 240, 270 300, 330, 360. This is why the system of degrees is based on a circle! BACK NEXT EXIT

  18. Q: Can we ever rotate the initial side counterclockwise more than one revolution? Answer – YES! BACK NEXT EXIT

  19. Note: Complete RevolutionsRotating the initial side counter-clockwise 1 rev., 2 revs., 3revs., . . . generates the angles which measure 360, 720, 1080, . . . BACK NEXT EXIT

  20. Picture BACK NEXT EXIT

  21. In fact, rotating the initial side counter-clockwise n revolutions (from 0) generates the angles n  360 BACK NEXT EXIT

  22. Q: What if we start at 30, and now rotate our terminal side 1 complete revolution. What angle did we generate? BACK NEXT EXIT

  23. Answer -- BACK NEXT EXIT

  24. What if we start at 30 and now rotate our terminal side counter-clockwise 1 rev., 2 revs., or 3 revs. BACK NEXT EXIT

  25. 1 Revolution -- a 390° 1 REV m() = 30+360m() = 390 BACK NEXT EXIT

  26. 2 Revolutions a 750° 2 REVS m() = 30+360+360m() = 30+2360m() = 30+720m() = 750 BACK NEXT EXIT

  27. 3 Revolutions a 1110° 3 REVS m() = 30+360+360+360m() = 30+3360m() = 30+1080m() = 1110 BACK NEXT EXIT

  28. Q: What if we start at 30 and rotate counterclockwise n revolutions? What angle does this generate? BACK NEXT EXIT

  29. Answer -- NOW, 30° a n REV m() = 30+360n BACK NEXT EXIT

  30. We can generalize this procedure. Let’s start at an angle , then rotate n rev counterclockwise. What formula is generated? NOW,  a  =  + n•360° n REV BACK NEXT EXIT

  31. Definition: Coterminal Angles Angles  and  are said to be coterminal if  n360 BACK NEXT EXIT

  32. Example– The following angles are coterminal: 0, 360, 720, 1080, . . .coterminal 30, 390, 750, 1110, . . .coterminal 45, 405, 765, 1125, . . .coterminal 60, 420, 780, 1140, . . .coterminal BACK NEXT EXIT

  33. End of Positive AnglesTitle V East Los Angeles College1301 Avenida Cesar ChavezMonterey Park, CA 91754Phone: (323) 265-8784Email Us At:menteprog@hotmail.comOur Website:http://www.matematicamente.org BACK NEXT EXIT

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