Question

find all solutions of the equation.
√3 tan(1/3)t = 1
ans: pi/2
I know you have to use the unit circle at the end of the problem, but Im getting stuck on changing to sine and cosine. Can anyone show me how to answer step by step? Please and thank you!

Answer 1

\[\sqrt{3} tan(\frac{1}{3}t) = 1\]
Divide both sides by \(\sqrt{3}\)
\[\frac{\sqrt{3} tan(\frac{1}{3}t)}{\sqrt{3}} = \frac{1}{\sqrt{3}}\]\[tan(\frac{1}{3}t) = \frac{1}{\sqrt{3}}\]
Take arctan for both sides.
\[tan^{-1}(tan(\frac{1}{3}t)) = tan^{-1}(\frac{1}{\sqrt{3}})\]\[\frac{1}{3}t = \frac{\pi}{3}\]I think you'll get there.