Question

Find all solutions in the interval \([0, 2\pi)\)

\(\sf 7 tan^3x - 21 tan x = 0\)

Answer 1

@sammixboo

Answer 2

Yeah I am not that good with pre-calc and I can't help with this. Some other stuff - I can.

So sorry!

Answer 3

:(

Answer 4

Maybe @ganeshie8 can help?

Answer 5

\(\large\tt \begin{align} \color{black}{7 tan^3x - 21 tan x = 0\\~\\
7 tanx (tan^2x- 3 ) = 0\\~\\
7 tanx = 0~~\And~~(tan^2x- 3 ) =0\\~\\
x = arctan(0)~~\And~~tan^2x =3\\~\\
x = 0^{\circ}~~\And~~tanx =\pm \sqrt{3}\\~\\
x = 0^{\circ}~~\And~~x =\pm \dfrac{\pi}{3}\\~\\




}\end{align}\)

Answer 6

does that make sense? @sleepyjess

Answer 7

No, not really

Answer 8

What part don't you understand?

Answer 9

\(\large \begin{align} \color{black}{7 \tan^3x - 21 \tan x = 0\\~\\
\small\text{Factor 7 tanx out:}\\
7 \tan x (\tan^2x- 3 ) = 0\\~\\
\small\text{We can see that either }7\tan x = 0 ~\text{ or }~ \tan^2x-3 = 0\text{, so}\\
7 \tan x = 0~~\text{or} ~~(tan^2x- 3 ) =0\\~\\

x = \arctan(0)~~\text{or}~~\tan^2x =3\\~\\
x = 0^{\circ}~~\text{or}~~\tan x =\pm \sqrt{3}\\~\\
x = 0^{\circ}~~\text{or}~~x =\pm \dfrac{\pi}{3}\\~\\
}\end{align}\)

Does that help at all?

Answer 10

Where does \(\tan^2x\) come from?

Answer 11

We started with \(7\tan^3x-21\tan x\) .

We factored 7 tan x out.

Like \(7u^3-21u\Longrightarrow7u ~(u^2-3)\)

Answer 12

Oh ok

Answer 13

ok, so everything makes sense now?

Answer 14

I think so, but that isn't one of the options.

Answer 15

interval is \([0, 2\pi)\)

So answer is actually \(x=0~~\text{or}~~x = \dfrac{\pi}{3}\)

Answer 16

hmm yeah something is missing

Answer 17

Here are the options, http://prntscr.com/5h4skx

Answer 18

@mathmath333 made a mistake. \(\tan x = \pm\sqrt3\cancel\longrightarrow x = \pm\dfrac{\pi}{3}\)

if \(\tan x = \pm\sqrt3\), then either \(\tan x = \sqrt3\) or \(\tan x = -\sqrt3\)

So we have \(\tan x = \sqrt3\) at \(x = \dfrac{\pi}{3}\) and \(x = \dfrac{4\pi}{3}\)

and we have \(\tan x = -\sqrt3\) at \(x = \dfrac{2\pi}{3}\) and \(x = \dfrac{5\pi}{3}\)

So that would be option C

Answer 19

Oh, and this: \(\tan x=0~~\longrightarrow~~x=0\) or \(x = \pi\)

Answer 20

you have the following solutions: \(x=0, \dfrac{\pi}{3}, \dfrac{2\pi}{3}, \dfrac{3\pi}{3}=\pi, \dfrac{4\pi}{3}, \dfrac{5\pi}{3}\)

Answer 21

Thanks for explaining that to me. Can you help on a couple more?

Answer 22

I have to go, sorry.

Start a new question.

Answer 23

Ok, thanks