Question 8

8. [Maximum mark: 8]

Consider the function $f(x) = \arccos x$ for $-1 \leq x \leq 1$.

(a) On the set of axes below sketch the graph of $y = f(x)$.
On your sketch clearly indicate the $y$-intercept and coordinates of the end points. [2]

(b) Solve $\arccos(x) + \arccos(x\sqrt{3}) = \frac{3\pi}{2}$, for $-\frac{1}{\sqrt{3}} \leq x \leq \frac{1}{\sqrt{3}}$. [6]