I'm running into a trigonometry wall in my Linear Algebra class. I'm given a transformation matrix that represents a rotation, and am asked to find the angle of rotation.
I know that the $\cos\theta = -0.8$ and that $\sin\theta = 0.6$. I should be able to find the answer through either $\arccos(-0.8)$ or $\arcsin(0.6)$, but they give me different answers. How would I be able to determine which one is the right one? I remember that $\arccos$ is defined for $[0, \pi]$ and arcsin for $[\frac{-\pi}{2},\frac{\pi}{2}]$, but don't see how to relate these to the right answer. The answers in the back of the book state that the answer is 2.5 rad, which is given by $\arccos(-0.8)$, but I'm not sure why that answer is the correct one vs. $\arcsin(0.6) = 0.64$ rad. Can someone help me understand the why one answer given is correct and the other one isn't?