Year 12s: what will be the first way you research your future options? >>

C3 Trig question

Jonario

Solve 8cotX - 3tanX = 2

I need help with the re-arranging

8 1/TanX - 3 tanX = 2

do I divide by tan?

Scroll to see replies

Reply 1

zcomputer5

Original post by Jonario

Solve 8cotX - 3tanX = 2

I need help with the re-arranging

8 1/TanX - 3 tanX = 2

do I divide by tan?

Try multiplying by tanx on both sides and rearrange a little, do you notice anything? Perhaps a substitution...?

Reply 2

Jonario

Original post by zcomputer5

Try multiplying by tanx on both sides and rearrange a little, do you notice anything? Perhaps a substitution...?

Ahh that just made it worse, I'm confused now D:

8(1/tan^2X) - 3tan^2X = 2Tan :s-smilie:

Has this got something to do with the double angle formulae?

Reply 3

zcomputer5

Original post by Jonario

Ahh that just made it worse, I'm confused now D:

8(1/tan^2X) - 3tan^2X = 2Tan :s-smilie:

Has this got something to do with the double angle formulae?

This is just an example but what is 2X(1/2)?
Now tell me what is AX(1/A)?
Now what is (Tanx)x(1/tanx)?

Reply 4

StephenP91

If you multiply by tanx, it just turns into a simple quadratic. Just call tanx, u and maybe that'll make more sense.

Where in the world did you get 2x from?

Reply 5

Jonario

Original post by zcomputer5

This is just an example but what is 2X(1/2)?
Now tell me what is AX(1/A)?
Now what is (Tanx)x(1/tanx)?

Is that relevant to the question? I'm totally confused now :frown:

soz

Reply 6

StephenP91

Original post by Jonario

Is that relevant to the question? I'm totally confused now :frown:

soz

Well he's basically saying that:

\dfrac{1}{Tanx} * Tanx = 1

Reply 7

Jonario

Original post by StephenP91

If you multiply by tanx, it just turns into a simple quadratic. Just call tanx, u and maybe that'll make more sense.

Where in the world did you get 2x from?

Tan to the power of 2 X ?

So when I multiply by Tan i'll get

8(1/tan^2 X ) - 3 tan^2 X = 2tan?

Reply 8

zcomputer5

Original post by StephenP91

If you multiply by tanx, it just turns into a simple quadratic. Just call tanx, u and maybe that'll make more sense.

Where in the world did you get 2x from?

I was trying to help him rather than just giving him the answer as if you read his last post you would of realise that he made a mistake multipling both sides through by tanx. Therefore I can him some example for him i.e. 1/2 X 2 =1!

Reply 9

Jonario

Original post by StephenP91

Well he's basically saying that:

\dfrac{1}{Tanx} * Tanx = 1

Oh my apologies, I didn't visualise it like that.

Reply 10

zcomputer5

Original post by Jonario

Tan to the power of 2 X ?

So when I multiply by Tan i'll get

8(1/tan^2 X ) - 3 tan^2 X = 2tan?

You get 8 -3 tan^2 X = 2tanx

Reply 11

Jonario

Original post by zcomputer5

You get 8 -3 tan^2 X = 2tanx

Yep :P

then I rearrange to get

3Tan^2X = 6 ?

Then I square root the 6 and find tan^-1 ?

Reply 12

TobeTheHero

Original post by zcomputer5

This is just an example but what is 2X(1/2)?
Now tell me what is AX(1/A)?
Now what is (Tanx)x(1/tanx)?

you're making him confused!

Reply 13

StephenP91

Original post by Jonario

Yep :P

then I rearrange to get

3Tan^2X = 6 ?

Then I square root the 6 and find tan^-1 ?

You've gone wrong. You end up with a quadratic equation. Let me show you.

\dfrac{8}{Tanx} - 3Tanx = 2

Multiply by Tanx

8 - 3Tan^{2}x = 2Tanx

Simply re-arrange.

3Tan^{2}x + 2Tanx - 8 = 0

Quadratic equation. You can either make a substitution to make it look like quadratics you've previously dealt with or simply factorise as it is. Makes no difference.

(edited 13 years ago)

Reply 14

zcomputer5

Original post by Jonario

Yep :P

then I rearrange to get

3Tan^2X = 6 ?

Then I square root the 6 and find tan^-1 ?

Since when did 8-2tanx=6?

No, to solve the quadratic its easiest to make a substitution, i.e. let Tanx=u to get
3u^2 +2u -8=0 perhaps you can solve it from here?

Reply 15

TobeTheHero

Original post by Jonario

Solve 8cotX - 3tanX = 2

I need help with the re-arranging

8 1/TanX - 3 tanX = 2

do I divide by tan?

tANX(8/TAnx - 3 tanx)= 2tan x

8-3tan^2(x)=2tanx

3tan^2(x)+2tanx - 8 = 0

and you solve the rest :smile:

Reply 16

zcomputer5

Original post by TobeTheHero

you're making him confused!

Well I thought that All A-level mathematians should be able to compute those fractions, I am pretty sure I learnt them for key stage 3 at school?

Reply 17

TobeTheHero

(3tanx-4)(tanx+2)=0

:smile:

Reply 18

Jonario

Original post by zcomputer5

Since when did 8-2tanx=6?

No, to solve the quadratic its easiest to make a substitution, i.e. let Tanx=u to get
3u^2 +2u -8=0 perhaps you can solve it from here?