A curve is given parametrically as $x=4 \sin t$ and $y=4 \cos t$ for 0$\le$t $\le$2 $\pi$.How does the length change if the coefficients of x and y are doubled (meaning x = 8 sin t and y = 8 cos t)?
A)The length is doubled.
B)The length is halved
C)The length is increased by a factor of 4.
D)The length remains the same.

Question

Quizplus · Accepted Answer

Doubling the coefficients of $x$ and $y$ in the parametric equations scales the curve by a factor of 2, which doubles the length of the curve.

A Curve Is Given Parametrically As x=4sin⁡tx=4 \sin tx=4sint And y=4cos⁡ty=4 \cos ty=4cost

A Curve Is Given Parametrically As $x=4 \sin t$ And $y=4 \cos t$