Question

Find equations for the lines that are tangent and normal to the graph of y = sinx + 3 at x = pi

Answer 1

Now, the slope of the tangent line at any point (x,y) on the curve is just y'(x) = cosx

At x=pi, y' = -1 and y=3

So, we want the line through (pi,3) with slope -1.

y-3 = -(x-pi) = pi-x
y = -x + 3+pi

The slope of the normal line is -(1/-1) = 1

y-3 = (x-pi)
y = x + 3-pi