Question

Find the exact solution of the equation.
3arctan(2x) = π

Answer 1

start with \(\arctan(2x)=\frac{\pi}{3}\)

Answer 2

then what do i do

Answer 3

hmm that is a good question

Answer 4

maybe a good idea is to take the tangent of both sides

Answer 5

since \(\tan(\arctan(2x))=2x\) you get \(2x=\tan(\frac{\pi}{3})\)

Answer 6

now compute the \(\tan(\frac{\pi}{3})\) and then divide by 2

Answer 7

you should get
\[2x=\sqrt{3}\] and so \(x=\frac{\sqrt{3}}{2}\)

Answer 8

Thank you so much! This was very helpful! :)

Answer 9

yw