# `y = sin((pix)/2) + 1` Find the x-intercepts of the graph.

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### 1 Answer

`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.**