Question

what are the intercepts of the graph of f(x)=4cos^2 -3 on the interval [0, 2pi]?

Answer 1

I am sure you meant:
f(x)=4cos^2 x -3

for the x-intercepts:
4cos^2 x -3 = 0
cos^2 x = 3/4
cos x = ±√3/2 ---> so x is in all 4 quadrants.
I know that cos π/6 = √3/2

so x = π/6, π - π/6, π + π/6, and 2π-π/6
or
x = π/6, 5π/6, 7π/6, and 11π/6

for the y-intercept, let x = 0
f(0) = 4cos^2 0 - 3
= 4(1) - 3 = 1