Answer
a) $\frac{2\pi}{3}$
b) $-\frac{\pi}{4}$
c) $\frac{\pi}{4}$
Work Step by Step
a) First, we look at the interval of the inverse of cosine which is $0\lt x\lt \pi$. Then, we must find what angle will give a value of $-1/2$ in that interval. The answer is $\frac{2\pi}{3}$
b) First, we look at the interval of the inverse of sine which is $-\frac{\pi}{2}\lt x\lt\frac{\pi}{2}$. Then, we must find what angle will give a value of $-\sqrt2/2$ in that interval. The answer is $-\frac{\pi}{4}$
c) First, we look at the interval of the inverse of tangent which is $-\frac{\pi}{2}\lt x\lt\frac{\pi}{2}$. Then, we must find what angle will give a slope of $1$ in that interval. The answer is $\frac{\pi}{4}$
