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 $3 \pi /2$


Why not use a definition...?
According to Wikipedia Maxima and minima — Definition:

If the domain $X$ is a metric space then $f$ is said to have a local (or relative) [...] minimum point at $x^∗$ if [there exists some $ε > 0$ such that] $f(x^∗) ≤ f(x)$ for all $x$ in $X$ within distance $ε$ of $x^∗$

Of course $\pi/4$ fits the definition criteria: for any (sufficiently small) neighborhood of $\pi/4$, sine at that point is smaller than for any other point in the neghborhood. So $\pi/4$ is the local minimum point.
