Where are the x-intercepts for f(x) = −4cos(x − pi over 2) from x = 0 to x = 2π? (?

Consider the function 

the x-intercepts of the graph of f, are the zeros of f, that is the solutions of f(x)=0.

so we solve 





at this point we ask ourselves, keeping the unit circle in mind, "cosine of what is 0?"

In the unit circle, from 0 to 2π radians,

cos 90° = cos (π/2) rad = 0

and

cos 270° = cos (3π/2) rad = 0

this means that 

i)




and 

ii)




ii) also, check that is also 0, because cos (-pi/2)= cos (-90°)=cos 270°=0

 

x=0, x=π, and x=2π