4cos(2x-pi)=0 for -pi =< x =< pi

Question

Solve to find the x intercepts of the function

 

Answer 1

Cos(x) equals zero when x = pi/2 ± n·pi for n = 0, 1, 2, 3, ...  For -4cos(2x-pi) (the -4 doesn't affect the zeros), we must have:

 

2x - pi = pi/2 ± n·pi

2x = 3pi/2 ± n·pi

x = 3pi/4 ± n·pi/2

 

Plug in values for n (n = 0, 1, 2, 3, ..) to find all values of x between -pi and pi. There will be four of them, two positive and two negative.  Those are the x-intercepts.