Precalculus, Chapter 5, 5.3, Section 5.3, Problem 45

y= sin ((pix)/2) + 1
Before we solve for the x-intercepts, let's determine the period of this function.
Take note that if a trigonometric function has a form y= Asin(Bx + C) + D, its period is:
P e r i o d = (2pi)/B
If we plug-in the value of B, we will get:
P e r i o d = (2pi)/(pi/2) = ((2pi)/1)/(pi/2)=(2pi)/1* 2/pi=4
Hence, the period of the given function is 4.
Let's solve now the x-intercepts. To solve, set y=0.
y= sin ((pix)/2) + 1
0=sin((pix)/2) + 1
-1= sin ((pix)/2)
Take note that sine has a value of -1 at an angle (3pi)/2 .
(3pi)/2 = (pix)/2
Then, isolate the x.
(3pi)/2*2/pi = (pix)/2*2/pi
3=x
Since the period of the function is 4, therefore the x-intercepts are:
x= 3 + 4n
where n is any integer.