On the graph of fx sin x and the interval 2pi 4 pi for what

On the graph of f(x) = sin x and the interval [2pi, 4 pi), for what value of x does f(x) achieve a maximum? Choose answers that apply. Answers 2pi 5pi/4 5pi/2 5pi 7pi/2

Solution

we know that sin(x) can have maximum value 1 which occurs at x=pi/2
and that repeats after every 2pi interval because period of sin(x) is 2pi
we need answer in interval [2pi,4pi)
pi/2 doesn\'t belong to that interval so add 2pi into pi/2
we get 5pi/2 which clearly belongs to given interval [2pi,4pi)
Hence 5pi/2 is the final answer.