Find out the length of the parametric curve illustrated by the following parametric equations.

x = 3sin (t)

y = 3 cos (t)

0 ≤ t ≤ 2?

Solution

We make out that this is a circle of radius 3 centered at the basis from our prior discussion about graphing parametric curves.  We as well know from this discussion that it will be traced out exactly one in this range.

Thus, we can make use of the formula we derived above.  We'll first require the following,

 dx/dt = 3 cos (t)

 dy/dt = -3sin (t)

after that the length is