I want to tell something about sinusoidal translation. For sketching a graph for sinusoidal translating we must know about amplitude, period, vertical and horizontal shifts.
Amplitude is distant max+min/2 and it is the distance between the middle of the graph to min or max.
The period is one cycle when our graph starts moving and reach the place which the graph was at first its a cycle.
The vertical shift is +y or -y and the horizontal shift is -(-x) or-(x).