Consider the general form of a transformed sine function, y=asin b(x-h)+k.
Practice makes perfect
Let's consider the given function.
y=3sin 2(x+π/2)-5
Now we will compare our function with the general form of a transformed sine function.
General Form
y= a sin b(x- h)+ k
Given Function
y= 3 sin 2 (x-( - π/2))+( - 5)
Because a= 3 and b= 2, the desired graph is a translation of y= 3sin 2x. This is a horizontal shrink by a factor of 1 2 and a vertical stretch by a factor of 4 of the graph of its parent function, y=sin x. Let's sketch this function.
Since k= - 5, the graph of the given function translates the graph of y=3sin 2x down by 5 units. The horizontal translation of a periodic function is called a phase shift. Therefore, h= - π2 tells us that there is a phase shift of π2 units to the left.
Finally, we will draw the obtained graph in the interval from 0 to 2π. We will extend the current pattern to 2π and restrict the domain to only positive values of x.
