Mathematics

Problem

Consider the function

f

defined by

f(\theta)=2\sin \theta

for

\theta\in\left[-\dfrac{\pi}{2},\dfrac{3\pi}{2}\right]

. a. (i) Determine the domain and the range of

f

. b. (ii) Find the

\theta

-coordinates of all points in the given interval at which

f

attains its maximum and minimum values. State the corresponding maximum and minimum values. c. (iii) Find all points where the graph of

y = f(\theta)

meets the

\theta

-axis in the stated interval. d. (iv) Draw a rough sketch of the graph of

y = f(\theta)

in the given interval, clearly marking the intercepts and the extreme points.