Question

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

Answer 1

We have

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

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

`-(3\pi)/(4)+2\pi=(5\pi)/(4)`

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

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

ANSWER

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