Sketching Tangent and Normal Lines Together with the Function

How to define a function?

How to sketch the graph of the function?

How to find the equation of the tangent line?

Equation of the tangent line to the graph of the function f(x) at the point x=a is g(x)=f'(a)(x-a)+f(a). Using this formula we have

How to graph the function together with the tangent line at a point?

How to find the equation of the normal line?

Equation of the normal line to the graph of the function f(x) at the point x=a is g(x)=+f(a). Using this formula we have

Homework

Problem 1

Consider the function f(x) = sin (x).

(a) Find the equation of the tangent line at x = .

(b) Find the equation of the normal line at x = .

(c) Sketch the graphs of the function, the tangent line, and the normal line on the same xy-plane.