PRECALCULUS:GRAPHICAL,...-NASTA ED.
10th Edition
ISBN: 9780134672090
Author: Demana
Publisher: PEARSON
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Expert Solution & Answer
Chapter 6.3, Problem 62E
Solution
To find: The correct option from the given options.
The correct option is (A).
Given information:
The expression is x=2cost , y=2sint ; t=2π3 .
Calculation:
Substitute 2π3 for t in parametric equations: x=2cost , y=2sint
(x,y)=(2cost,2sint)=(2cos(2π3),2sin(2π3))=(2cos(π−π3),2sin(π−π3))=(−2cos(π3),2sin(π3))
Therefore, the point corresponds to t=2π3 in the parametrization x=2cost , y=2sint ; is (−2cos(π3),2sin(π3)) .
Substitute −4π3 for t in parametric equations: x=2cost , y=2sint :
(x,y)=(2cost,2sint)=(2cos(−4π3),2sin(−4π3))=(2cos(4π3),−2sin(4π3))=(2cos(π+π3),−2sin(π+π3))=(−2cos(π3),2sin(π3))
Substitute −2π3 for t in parametric equations: x=2cost , y=2sint :
(x,y)=(2cost,2sint)=(2cos(−2π3),2sin(−2π3))=(2cos(2π3),−2sin(2π3))=(2cos(π−π3),−2sin(π−π3))=(−2cos(π3),−2sin(π3))
Substitute −π3 for t in parametric equations: x=2cost , y=2sint :
(x,y)=(2cost,2sint)=(2cos(−π3),2sin(−π3))=(2cos(π3),−2sin(π3))
Substitute 4π3 for t in parametric equations: x=2cost , y=2sint :
(x,y)=(2cost,2sint)=(2cos(4π3),2sin(4π3))=(2cos(π+π3),2sin(π+π3))=(−2cos(π3),−2sin(π3))
Thus, the point corresponds to t=2π3 and the point corresponds to t=−4π3 produces the same point for the parametrization: x=2cost , y=2sint ; namely, (−2cos(π3),2sin(π3)) .
Therefore, the correct option is (A).
Chapter 6 Solutions
PRECALCULUS:GRAPHICAL,...-NASTA ED.
Ch. 6.1 - Prob. 1QRCh. 6.1 - Prob. 2QRCh. 6.1 - Prob. 3QRCh. 6.1 - Prob. 4QRCh. 6.1 - Prob. 5QRCh. 6.1 - Prob. 6QRCh. 6.1 - Prob. 7QRCh. 6.1 - Prob. 8QRCh. 6.1 - Prob. 9QRCh. 6.1 - Prob. 10QR
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