Question

I need to solve this without a calculator
6tan \frac{ 1 }{ 3 }x =3sqrt{3}

from \[\left( 0, 2\pi\right)\]

Answer 1

is it \[\tan(\frac{1}{3}x)\]
or
\[\tan(\frac{1}{3})x\]
?

Answer 2

\[6\tan \frac{ 1 }{ 3 }x =3\sqrt{3}\]

Answer 3

so you are trying to solve

\[6 \tan(\frac{x}{3}) = 3 \sqrt{3}\]

Answer 4

divide both sides by 6

what do you get..?

Answer 5

but is the x inside or outside the tangent? that's kind of important

Answer 6

its inside...

Answer 7

I feel really bad. The tan is supposed to be sin. When i devide by 6 i get \[\sin \frac{ x }{ 3 }=\frac{ \sqrt{3} }{ 2 }\]

Answer 8

yep, so how do you reverse sin?

Answer 9

\[\frac{ 1 }{ \sin } or \csc \] ?

Answer 10

got it thanks

sometimes i make these harder than they need to be