Consider the function f(x)=sin(x) in the interval x=[π/4,7π/4]. The number and location(s) of the local minima of this function are? This is MCQ of a competitive exam(GATE), Answer is (d) given by GATE , and from other sources ,explanation is (b) somewhere and (d) somewhere , I am going with (b) as minimum at $270$, I have drawn graph . but it produces two pictures , I confused , it asked Local minima of a trivial $\sin(x)$ function and explanation here, but didn't get obviously , finally I want to explanation . 
Problem is :

Consider the function $f(x)=\sin(x)$ in the interval $x=[\pi /4,7 \pi /4]$. The
  number and location(s) of the local minima of this function are
(A) One, at $\pi /2$ 
(B) One, at $3 \pi /2$ 
(C) Two, at $ \pi /2$ and $3 \pi /2$
(D) Two, at $\pi /4$ and $3 \pi /2$


The local minima is at $x=\frac{3\pi}{2}$
This is very obvious from the graph of $f(x)=\sin{x}$
On a second look at the graph below, I believe $x=\frac{\pi}{4}$ is also a local minimum. This is because it is lesser than all other values within its locality. 
Thus we have two local minima: $x=\frac{\pi}{4}, \frac{3\pi}{2}$

