Assume time t runs from zero to 2π and that the unit circle has been labled as a clock. Match each of the pairs of parametric equations with the best description of the curve from the following list. Enter the appropriate letter (A, B, C, D, E, F ) in each blank. A. Starts at 12 o'clock and moves clockwise one time around. B. Starts at 6 o'clock and moves clockwise one time around. C. Starts at 3 o'clock and moves clockwise one time around. D. Starts at 9 o'clock and moves counterclockwise one time around. E. Starts at 3 o'clock and moves counterclockwise two times around. F. Starts at 3 o'clock and moves counterclockwise to 9 o'clock. 1. x=cos(2t); y=sin(2t) 2. x=sin(t); y=cos(t) 3. x=cos(t); y=−sin(t) 4. x=−sin(t); y=−cos(t) 5. x=−cos(t); y=−sin(t)

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Answer:

1 = D

2= B

3 = C

4 = A

5 = F

Step-by-step explanation:

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Following are the calculation to the given points:

  • Starts at 12 o'clock in the morning and travels clockwise once. [tex]x=\sin(t); y=\cos(t)\\\\[/tex]
  • Starting at 6 o'clock then make your way clockwise once.
  • [tex]x=-\sin(t); y=-\cos(t) \\\\[/tex]
  • Starting at  3 o'clock then make your way clockwise once.
  • [tex]x=\cos(t); y=-\sin(t) \\\\[/tex]
  • Starting at 9 o'clock and rotates counterclockwise once.
  • [tex]x=-\cos(t); y=-\sin(t)\\\\[/tex]
  • Starting at 3 o'clock and work your way counterclockwise to 9 o'clock. [tex]x=\cos(\frac{t}{2}); y= \sin (\frac{t}{2}) \\\\[/tex]

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