Mathematics

Problem

A point

P

lies on the curve

y=\sec x

with

x=\tfrac{\pi}{4}

. All coordinates use radians. (a) Calculate the slope of the tangent line to the curve at point

P

. (b) Write an equation for the tangent line at

P

in point–slope form. (c) Write an equation for the line normal to the curve at

P

. (d) Determine the

y

-intercept of the tangent line found in part (b).