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C2 Trig help

I'm not sure how to do this question, I got as far as rearranging the formula to tanx=3/root3

How do you get to the step with tanx=1/root3

Help would be appreciated.

I've attached the question and the mark scheme answer

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Original post by smooo

I'm not sure how to do this question, I got as far as rearranging the formula to tanx=3/root3

How do you get to the step with tanx=1/root3

Help would be appreciated.

I've attached the question and the mark scheme answer

What is root 3 x root 3? Does that help?

Original post by smooo

I'm not sure how to do this question, I got as far as rearranging the formula to tanx=3/root3

How do you get to the step with tanx=1/root3

Help would be appreciated.

I've attached the question and the mark scheme answer

Its root3/3 not 3/root3 and root3/3=1/root3

Original post by veejn

Its root3/3 not 3/root3 and root3/3=1/root3

Uhm, your intial post is wrong.

You have

3\tan x - \sqrt{3} = 0

. Add

\sqrt{3}

to both sides:

3\tan x = \sqrt{3}

.

Now divide throughout by

3

to get

\tan x = \frac{\sqrt{3}}{3} \neq \frac{3}{\sqrt{3}}

.

Anyways, we have

\tan x = \frac{\sqrt{3}}{3}

.

Now two ways to think about this:

1) indices rules:

\frac{\sqrt{3}}{3} = \frac{3^{1/2}}{3^1} = 3^{1/2 - 1} = 3^{-1/2} = \frac{1}{3^{1/2}}= \frac{1}{\sqrt{3}}

2) multiply top and bottom by

\sqrt{3}

:

\frac{\sqrt{3}\sqrt{3}}{3\sqrt{3}} = \frac{3}{3\sqrt{3}} = \frac{1}{\sqrt{3}}

OP

Original post by Zacken

Uhm, your intial post is wrong.

You have

3\tan x - \sqrt{3} = 0

. Add

\sqrt{3}

to both sides:

3\tan x = \sqrt{3}

.

Now divide throughout by

3

to get

\tan x = \frac{\sqrt{3}}{3} \neq \frac{3}{\sqrt{3}}

.

Anyways, we have

\tan x = \frac{\sqrt{3}}{3}

.

Now two ways to think about this:

1) indices rules:

\frac{\sqrt{3}}{3} = \frac{3^{1/2}}{3^1} = 3^{1/2 - 1} = 3^{-1/2} = \frac{1}{3^{1/2}}= \frac{1}{\sqrt{3}}

2) multiply top and bottom by

\sqrt{3}

:

\frac{\sqrt{3}\sqrt{3}}{3\sqrt{3}} = \frac{3}{3\sqrt{3}} = \frac{1}{\sqrt{3}}

Ah ok I get it now that you have to use indices, thank you.

Original post by smooo

Ah ok I get it now that you have to use indices, thank you.

You don't have to use indices, I've given you two different ways to think about it. But sure, no problem.

Original post by Zacken

You don't have to use indices, I've given you two different ways to think about it. But sure, no problem.

To be fair, if you plugged in root 3 / 3 or 1 / root 3 into your calculator you'd still get the same solutions

Original post by Rhy

To be fair, if you plugged in root 3 / 3 or 1 / root 3 into your calculator you'd still get the same solutions

Yes, that was the point of my post, demonstrating their equivalency.

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