2.1: Tangent curve constants and cosine graph

Given that $y = a\tan bx + c$ has period $\tfrac{\pi}{4}$ radians and passes through the points $(0, -2)$ and $\left(\tfrac{\pi}{16}, 0\right)$, find the value of each of the constants $a$, $b$ and $c$.

On the axes below, draw the graph of $y = 2\cos 3x + 1$ for $-\tfrac{2\pi}{3} \le x \le \tfrac{2\pi}{3}$ radians.

Using your graph, or otherwise, find the exact solutions of $(2\cos 3x + 1)^{2} = 1$ for $-\tfrac{2\pi}{3} \le x \le \tfrac{2\pi}{3}$ radians.