Simple Trig Question- Need an explanation as to why two of these options work

[toniB]

Cos(x)= k where k is radian measure of an angle and
π<x <3π/2

If cos(z)= -k why does these two options work as z?

1) x-π
2)3π- x

[FONT=arial, sans-serif-light, sans-serif]Thank you very muching for the helping[/FONT]

 

[stapel]

Suppose that cos(x) = k, where x is in radians and is the measure of an angle on the interval \(\displaystyle \,\pi\, <\, x\, <\, \dfrac{3\pi}{2}.\)

My question: If cos(z) = -k, why do these two options work as solution intervals for z?

\(\displaystyle 1)\, x\, -\, \pi\)

\(\displaystyle 2)\, 3\pi\, -\, x\)

Thank you very much for your help.

What did you see when you look at the graph of the cosine wave? Where does the cosine repeat its values? How does this repetition relate to pi and 3pi, on the graph?