Exercise 61 Page 926

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.