Question

At what x-values do the graphs of the functions y=cos 2x and y = cos^2 x-1 intersect over the interval 0 ≤ x ≤ pi. There must be two selections there are two anwsers!

Answer 1

x=pi/2 and x=3pi/2

Explanation:

Answer 2

`x=(\pi)/(2)` and
`x=(3\pi)/(2)`

Explanation:

We need to solve the 2 equations to figure out the x-values (intersecting points).

Note: The identity
`cos^(2)x=(1)/(2)+(1)/(2)cos(2x)`

`cos(2x)=cos^(2)(x)-1\\cos(2x)=((1)/(2)+(1)/(2)cos(2x))-1\\cos(2x)=(1)/(2)cos(2x)-(1)/(2)\\(1)/(2)cos(2x)=-(1)/(2)\\cos(2x)=-1\\2x=cos^(-1)(-1)\\2x=\pi, 3\pi\\x=(\pi)/(2), (3\pi)/(2)`

So they intersect at
`x=(\pi)/(2), (3\pi)/(2)`