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 eq
uations 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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Given:
The function is:
To find:
The value of .
Solution:
We have,
Putting , we get
On combining like terms, we get
Therefore, the required function is .