00:01
Hello students, in this question we have to find the slope of the tangent line to the polar curve.
00:06
Here the polar curve is given that r equal to 8 cos theta.
00:21
Here we have to find the slope so that we have to find dy by dx.
00:26
Here r equal to 8 cos theta is a circle so let us consider x equal to r cos theta and y equal to r sin theta.
00:35
Here we can replace r by 8 cos theta such that x equal to r cos theta which is written as 8 cos theta into cos theta such that we will get x equal to 8 cos square theta.
00:54
Then y equal to r sin theta.
00:57
Here we have to replace r by 8 cos theta into sin theta which is y.
01:06
So we need to find dx by d theta and dy by d theta.
01:13
So dx by d theta is 16 cos theta into minus sin theta.
01:29
So we can say that it is minus 16 cos theta sin theta which is dx by d theta.
01:36
Then we have to find dy by d theta which is equal to, so dy by d theta is minus sin square theta plus cos square theta...