Sketch the graph of f(x) = 2 2 sin x on the interval [0, /2]. (a) Find the distance from the origin to the

Sketch the graph of f(x) = 2 − 2 sin x on the interval [0, π/2]. 

(a) Find the distance from the origin to the y-intercept and the distance from the origin to the x-intercept.

(b) Write the distance d from the origin to a point on the graph of f as a function of x.

(c) Use calculus to find the value of x that minimizes the function d on the interval [0, π/2]. What is the minimum distance? Use a graphing utility to verify your results.