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Further Maths question sin cos tan

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1. I don't understand the last question, question 17 on this paper

http://filestore.aqa.org.uk/subjects...P-QP-JUN15.PDF

Please can someone tell me how to do it, not just the answer but an explanation?

The mark scheme is here
http://filestore.aqa.org.uk/subjects...W-MS-JUN15.PDF

Thank you
2. (Original post by jazz_xox_)
I don't understand the last question, question 17 on this paper

http://filestore.aqa.org.uk/subjects...P-QP-JUN15.PDF

Please can someone tell me how to do it, not just the answer but an explanation?

The mark scheme is here
http://filestore.aqa.org.uk/subjects...W-MS-JUN15.PDF

Thank you
Which bit are you stuck with?

First thing to do would be to have a look at the denominator and think of an identity, and go from from there.
3. Look at and rearrange any identities you have learnt and then see if you can substitute any of the expressions
4. (Original post by SeanFM)
Which bit are you stuck with?

First thing to do would be to have a look at the denominator and think of an identity, and go from from there.
All of it I don't understand or know the identities, do you know where there is a list of them? I think i missed a lesson on this and I don't understand it at all
5. (Original post by ravioliyears)
Look at and rearrange any identities you have learnt and then see if you can substitute any of the expressions
thanks, do you know where i can find a list of the identities that i can learn?
6. (Original post by jazz_xox_)
thanks, do you know where i can find a list of the identities that i can learn?
Literally just cos^2 x + sin^2 x = 1.

Can you think of how to use this in your question? (hint: re-arrange the above identity).
7. (Original post by jazz_xox_)
thanks, do you know where i can find a list of the identities that i can learn?
You don't need to learn them - all the ones you need to know are on the second page of the paper - on the equations sheet.

No problem
8. (Original post by jazz_xox_)
thanks, do you know where i can find a list of the identities that i can learn?
The only ones you should need are:

sinx / cosx = tanx

sin2x + cos2x = 1
9. (Original post by ravioliyears)
You don't need to learn them - all the ones you need to know are on the second page of the paper - on the equations sheet.

No problem
thank you!
10. (Original post by jazz_xox_)
I don't understand the last question, question 17 on this paper

http://filestore.aqa.org.uk/subjects...P-QP-JUN15.PDF

Please can someone tell me how to do it, not just the answer but an explanation?

The mark scheme is here
http://filestore.aqa.org.uk/subjects...W-MS-JUN15.PDF

Thank you
Basically, you need to write : LHS = 2tan squared theta + 1 first.
Then, what I normally do is write the two trigonometric identities, so tan theta = sin theta/cos theta and sin squared theta + cos squared theta =1.

Now, we know that tan theta is equal to sin theta/cos theta, therefore, use the same principle to get tan squared theta = sin squared theta/cos squared theta. However, as there's a 2 infront of the tan squared theta, you need ot double this like a normal fraction to get 2sin^2 theta / cos squared theta +....1 (this is the 1 that's left over - we haven't touched this).

Now you should have a fraction that looks like: (2Sin^2 Theta/Cos^2 Theta) + 1. Now we want to include the 1 in the whole fraction, so just do it like a normal fraction. Make the denominator of the 1 become cos^2 theta, by multiplying it by cos^2 theta. Hence, you end up witth (2sin^2 theta + cos^2 theta)/ cos ^2 theta.

Now if you rearrange the bottom of this, using sin^2 theta + cos ^2 theta = 1 (a trigonmetric identity), you know that cos ^2 theta = 1-sin^2 theta. Hence, you've got the denominator sorted.

Then, break up the numerator, to get sin ^2 theta + sin^2 theta + cos^2 theta INSTEAD of 2sin^2 theta + cos^2 theta. Now we know that sin^2 theta + cos ^2 theta =1. Therefore, the sin^2 theta + cos^2 becomes 1 , leaving you with 1 + sin^2 theta.

Now both parts should match the RHS so just say that.
Simples.
If this helped repping me would be appreciated, thanks.
11. (Original post by jazz_xox_)
thank you!
12. (Original post by Alexion)
The only ones you should need are:

sinx / cosx = tanx

sin2x + cos2x = 1
They're on the equations sheet on the exam booklet for GCSE FM although jazz_xox_ you'll need to learn them for A-Level C2 Maths
13. (Original post by jazz_xox_)
All of it I don't understand or know the identities, do you know where there is a list of them? I think i missed a lesson on this and I don't understand it at all
I cheated and used an A-level identity for this but it seems you can do it without it.

http://filestore.aqa.org.uk/subjects/AQA-8360-W-SP.PDF

Spec - bullet point 6.9. Those are the only two things you need to know, it seems, and that they are given in the exam.
14. (Original post by Zacken)
Literally just cos^2 x + sin^2 x = 1.

Can you think of how to use this in your question? (hint: re-arrange the above identity).
do you sub in cos^2 x + sin^2 x for the 1?
i'm probably on the wrong track, i don't get it at all!
15. (Original post by jazz_xox_)
do you sub in cos^2 x + sin^2 x for the 1?
i'm probably on the wrong track, i don't get it at all!
Well... a more direct way to think of it is that if you can write cos^2 x + sin^2 x = 1, then you can re-arrange this to say that 1 - sin^2 x = cos^2 x. So you can replace the 1-sin^2 x in the denominator with cos^2 x.
16. (Original post by SeanFM)
I cheated and used an A-level identity for this but it seems you can do it without it.

http://filestore.aqa.org.uk/subjects/AQA-8360-W-SP.PDF

Spec - bullet point 6.9. Those are the only two things you need to know, it seems, and that they are given in the exam.
Okay thank you that helps a lot!

I've ended up with
2 sin ^2 x / cos^2 x +1 (which is the first mark on the mark scheme)
but I am unsure how to prove that this is identical to what I'm given?
17. (Original post by Zacken)
Well... a more direct way to think of it is that if you can write cos^2 x + sin^2 x = 1, then you can re-arrange this to say that 1 - sin^2 x = cos^2 x. So you can replace the 1-sin^2 x in the denominator with cos^2 x.
Yes I've got that now, but I don't understand how to prove that this is identical to what I'm given?
18. (Original post by jazz_xox_)
Okay thank you that helps a lot!

I've ended up with
2 sin ^2 x / cos^2 x +1 (which is the first mark on the mark scheme)
but I am unsure how to prove that this is identical to what I'm given?
I see you are getting help from different angles (ha) so I will leave it to someone else so that you are not confused.

Good luck!
19. (Original post by SeanFM)
I see you are getting help from different angles (ha) so I will leave it to someone else so that you are not confused.

Good luck!
Haha thank you. Could you please tell me how this could be identical to 1+sin^2x / 1- sin^2 x ?

Sorry for being a pain thankk you
20. (Original post by jazz_xox_)
Yes I've got that now, but I don't understand how to prove that this is identical to what I'm given?
Do you know that if you have (a+b)/c, you can split it into a/c + b/c?

If so, you now (1+sin^2 x) / cos^2 x.

You can split this into (1/cos^2 x) + (sin^2 x / cos^2 x).

But you know what (sin x / cos x) is, so you should know what (sin x / cos x)^2, is.

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