An equation is given. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal places where appropriate. If there is no solution, enter …

Question

asked Mar 21, 2020 41.1k views

1 Answer

Ben Hymers · Answer 1 · 2020-03-25T11:28:48+0000

$3\tan3\theta-1=0$

$3\tan3\theta=1$

$\tan3\theta=\frac13$

Recall that the tangent function has a period of
$\pi$ so that

$3\theta=\tan^(-1)\frac13+k\pi$

for any integer
. Then

$\theta=\frac13\tan^(-1)\frac13+\frac{k\pi}3$

We get 6 solutions in the interval [0, 2π) for
$0\le k\le5$ ,

$\theta\approx0.107$

$\theta\approx1.154$

$\theta\approx2.202$

$\theta\approx3.249$

$\theta\approx4.296$

$\theta\approx5.343$