I was given the following problem on a quiz:
I put A, C, and D. The answer was A and D. We were taught four relevant equations:
$\sin(x)=-\sin(-x)$
$\cos(x)=\cos(-x)$
$\sin(x)=\cos(x-\frac{\pi}{2})$
$\cos(x)=\sin(x+\frac{\pi}{2})$
Based on my understanding of the unit circle definitions of cosine, and the appearance of the graphs of sine and cosine, I assumed:
$-\cos(x)=\cos(x\pm\pi)$
That's part of how I got C as an answer. I also graphed my answers after the quiz and they all looked the same.
Was my assumption wrong? Is there something I'm missing?
I also checked Wikipedia, which says:
$\cos(\pi-\theta)=-\cos(\theta)$
http://en.wikipedia.org/wiki/List_of_trigonometric_identities