`y = sin(pix) + cos(pix)` Find the x-intercepts of the graph.
You need to evaluate the x intercepts of the graph, hence, you need to remember that the graph intercepts x axis at y = 0. Hence, you need to solve for x the equation `y= f(x) = 0` .
`sin pi*x + cos pi*x = 0`
You need to divide by `cos pi*x` , such that:
`(sin pi*x)/(cos pi*x) + 1 = 0`
`tan pi*x = -1 => pi*x = arctan (-1) + k*pi`
`pi*x = -pi/4 + k*pi`
Dividing by `pi` both sides, yields:
`x = -1/4 + k`
Hence, evaluating the x intercepts of the graph of the given function, yields `x = k - 1/4` , where` k in Z` .