find the minimum value of , hence find smallest positive value of x where the minimun value occurs.
You know the range for the graph y = sin(x) is [-1, 1]. For your question, you should know that the -40 inside the brackets will not affect the vertical shifting of the graph. So:
To find what x values occur at the max and min, just set your expression equal to them
Are you aware of stretches of translations of graphs ?
first can you draw ? with reasonable accuracy showing where it is zero and the min/max points between -360 to 360. If you draw this graph well the rest of the problem is very easy.
If you can do that then, you need to understand that is stretched vertically. and that is a horizontal shift.