00:01
Hi, in this question we have the transformation for converting the cartesian coordinate of x ,y into the polar coordinate of r ,theta.
00:10
So that is our x is equal to r cos theta, y is equal to r sin theta and r square is equal to x square plus y square.
00:20
So in part a, the given the cartesian coordinate is x ,y is equal to 1 ,root 3.
00:28
So with r is greater than 0 and 0 less than or equal to theta less than 2 pi.
00:37
Then tan theta is equal to y by x is equal to root 3 by 1.
00:44
So which implies tan theta is equal to root 3.
00:48
So theta is equal to tan inverse of root 3.
00:52
So theta is equal to pi by 3 and r is equal to root of x square plus y square which is equal to root of 1 plus 3 root of 4 that is 2.
01:04
So therefore the required polar coordinate is r ,theta is equal to 2 ,pi by 3 and part b, the given x ,y is equal to tan theta is equal to tan inverse of minus root 3 is minus pi by 3 and r is x square plus y square.
01:28
So minus 4 the whole square plus 4 root the whole square is root 64 that is 8...