Question

Find the value of
tan(3Arc cos3/4)

Answer 1

\(\arccos \frac{3}{4}\) is an angle, so let \(\theta = \arccos \frac{3}{4} \implies \cos \theta = \frac{3}{4}\)

so hypoteneous = 4, adjacent side = 3 means opposite side, from Pythagoreas, \(= \sqrt{7}\)

Hence \(\tan \theta = \dfrac{\sqrt7}{3}\)


Next use this:


\( \tan 3\theta = \dfrac{3 \tan\theta - \tan^3\theta}{1 - 3 \tan^2\theta}
\)

\( = \dfrac{3 \frac{\sqrt7}{3} - (\frac{\sqrt7}{3})^3}{1 - 3 (\frac{\sqrt7}{3})^2} \)

\(= -\dfrac{5 \sqrt(7)}{ 9}\)

\(tan 3 \theta\) can be found using tan double angle formula