Question

how do you know cos(-3pi/4) = cos(5pi/4)

Answer 1

We have

$\cos (-\frac{3\pi}{4})=-\frac{\sqrt[]{2}}{2}$

in this case -3pi/4 and 5pi/4 are coterminal angles

$-\frac{3\pi}{4}+2\pi=\frac{5\pi}{4}$

therefore because they are coterminal angles the value of the cosine will be the same

$\cos (\frac{5\pi}{4})=-\frac{\sqrt[]{2}}{2}$

ANSWER

because they are coterminal angles the value of the cosine will be the same