To determine if a point is on a curve, we literally just stick the point in for the respective variables. In this case, 13 Pi halves is on the given curve. To find the tangent line, we need to find the slope. So we're going to find the derivative of the curve, remembering to use the product role when we have two variables that are multiplied together. So we have the derivative in terms of X of two XY. So we're going to take two times the derivative of X in terms of X * y + 2 X times the derivative of Y in terms of X. Plus we're going to have the derivative of π sine Y. So we're going to have π the derivative of sine is cosine, but then we also have to do the derivative of the inside piece using the chain rule. So the derivative of Y in terms of X. And then that's going to equal 0 SO2Y plus 2X DYD X + π cosine YDYDX all equals 0. Then we're going to get all the DYDXS on one side by themselves and factor out the DYDX. Everything else goes to the other side. And then we're going to divide. So we get DYDX equal -2 Y over two X + π cosine Y, putting in the point that was given of 1/3 Pi halves. So we put one in every time we see X and three Pi halves every time we see Y, and simplifying we get the -3π / 2. So to write the tangent line, we're just going to use point slope y -, 3 Pi halves equaling -3 Pi halves times the quantity X - 1. Computing that through to get Y equal. To find the normal line, we're going to take the perpendicular slope. So we're going to take the negative reciprocal of -3 Pi halves and use 2 / 3 Pi distributing and solving for Y.