Find the equation of a sine wave that is obtained by shiftin

Find the equation of a sine wave that is obtained by shifting the graph of y=sin x to the right 2 units and downward 1 unit, and that is vertically compressed by a factor of 2 when compared to y= sin x

Solution

y=sin x shifting to the right 2 units and downward 1 unit, and that is vertically compressed by a factor of 2

i) y = sin(x-2)

ii) downward 1 unit : y = sin(x-2) -1

iii) vertically compressed by a factor of 2 : y = (1/2)sin(x-2) -1

y = 0.5sin(x-2) -1