#1**+1 **

We need to find the slope of the line

dy/dx = dy/dt / dx/dt = cost / - sin t = - cot t

At t = pi/4, the slope is - cot (pi/4) = - 1

The normal line will have a slope of 1

The point is given by ( cos pi/4, sin pi/4) = ( sqrt (2)/2, sqrt (2)/2 )

So....the equation of the tangent lne is

y = 1 (x - sqrt (2) /2 ) + sqrt(2)/2

y = x

Here's the graph :

CPhill Dec 20, 2018