Yes I think you are right

y=2sin(3t-(pie)/4)+8between (pie) and 4(pie)

y=2sin(3t-(pie)/4)+8 for which y attains the minimum value.

thanks guys

RoboStar

Minimum value of function is -1. So minimum value of y could be 6.The real question is does there exist a t between (pie) and (4pie), such that this happens.

sin(3t-(pie)/4) = -1 means that

Thus

So

In general

So between an , we have three angles that satisfy:

and the minimum value is