Question

write the given expression in algebraic form: tan(arccos(x/3))

Answer 1

\[\Large \tan\left(\color{royalblue}{\arccos\frac{x}{3}}\right)\]So let's deal with the blue part first. We need to make a triangle with it.\[\Large \color{royalblue}{\arccos\frac{x}{3}=\theta} \qquad\to\qquad \cos \theta=\frac{x}{3}\]

Answer 2

\[\Large \cos \theta=\frac{adjacent}{hypotenuse}\]

Answer 3

\[\Large \tan\left(\color{royalblue}{\arccos\frac{x}{3}}\right) \qquad\to\qquad \tan\left(\color{royalblue}{\theta}\right)=\frac{opposite}{adjacent}\]

Answer 4

Gotta find that missing side