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Please help me with this Maths question!

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I know you have to use simultaneous equation, but I have no idea where to start. I don't think we've even covered this in class. Could anyone give me some hints on how I go about answering this question?

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Reply 1
Original post by Mystelle
I know you have to use simultaneous equation, but I have no idea where to start. I don't think we've even covered this in class. Could anyone give me some hints on how I go about answering this question?


This is quite a unique question. I decided to do it by substituting one into the other.

I started by rewriting the xx equation in terms of cosθ\cos\theta using the double angle formulae, then rearranging the yy equation for cosθ\cos\theta. You can then do some substitution to get it just in terms of yy
Reply 2
Original post by Ed5
This is quite a unique question. I decided to do it by substituting one into the other.

I started by rewriting the xx equation in terms of cosθ\cos\theta using the double angle formulae, then rearranging the yy equation for cosθ\cos\theta. You can then do some substitution to get it just in terms of yy


Is this C3 or C4?
Original post by Mystelle
Is this C3 or C4?


it's c3 trig identities
sin(theta)/cos(theta) = ta(theta)
iirc
Reply 5
Original post by Mystelle
Is this C3 or C4?


If you're on edexcel it's C3

The one you're looking for is cos(a+b)=cosacosbsinasinb\cos(a+b)=\cos{a}\cos{b} - \sin{a}\sin{b}

So when you shove in 2θ2\theta it becomes cos(θ+θ)=cos2θsin2θ\cos(\theta+\theta)=\cos^2{ \theta }-\sin^2{\theta}
(edited 6 years ago)
So ****ing happy I stopped doing Maths after High School.
Reply 7
Original post by Ed5
If you're on edexcel it's C3

The one you're looking for is cos(a+b)=cosacosbsinasinb\cos(a+b)=\cos{a}\cos{b} - \sin{a}\sin{b}

So when you shove in 2θ2\theta it becomes cos(θ+θ)=cos2θsin2θ\cos(\theta+\theta)=\cos^2{ \theta }-\sin^2{\theta}

Actually for Edexcel this would be C4 since it would come under the category of "parametric equations". You wouldn't see it in C3.
Reply 8
Original post by Notnek
Actually for Edexcel this would be C4 since it would come under the category of "parametric equations". You wouldn't see it in C3.


Yeah I was wondering where Parametric to Cartesian conversion came from... is there any way to tackle this question using C3 knowledge?
Reply 9
Original post by Mystelle
Yeah I was wondering where Parametric to Cartesian conversion came from... is there any way to tackle this question using C3 knowledge?

Yes. It will just be harder especially if this is the first one of these types of questions that you've done.

I recommend aiming to get both right-hand-sides in terms of cosθ\cos \theta only i.e. you can't have cos2θ\cos 2\theta or sinθ\sin \theta etc.

Do you know the three forms of the identity for cos2θ\cos 2\theta? One of them only has cosθ\cos \theta in it.
Reply 10
Original post by Mystelle
Yeah I was wondering where Parametric to Cartesian conversion came from... is there any way to tackle this question using C3 knowledge?

Out of interest, why are you doing C4 questions if you haven't learnt C4 yet?
Reply 11
Original post by King Leonidas
So ****ing happy I stopped doing Maths after High School.

How do you sleep at night knowing that there is so much mathematics that you haven't explored?
Reply 12
Original post by Notnek
Out of interest, why are you doing C4 questions if you haven't learnt C4 yet?


This was in my homework, as are a couple of C4 reverse chain rule questions, which we have been taught in class. But we've never gone through this sort of question before.

The only identities for cos(2theta) I know of are cos^(2)theta - sin^(2)theta, 2cos^(2)theta - 1 and 1 - 2sin^(2)theta.
(edited 6 years ago)
Original post by Notnek
How do you sleep at night knowing that there is so much mathematics that you haven't explored?

Just fine, as long as I can count that's the main thing:u:

Learning all those equations and symbols just seems mundane, and only a necessity for a career, which would require use of it.

Prepare your angus for this controversial comment:

Spoiler

Reply 14
Original post by Mystelle
This was in my homework, as are a couple of C4 reverse chain rule questions, which we have been taught in class. But we've never gone through this sort of question before.

The only identities for cos(2theta) I know of are cos^(2)theta - sin^(2)theta, 2cos^(2)theta - 1 and 1 - 2sin^(2)theta.

The second one is what you need since this is only in terms of cosθ\cos \theta. So you have

x=2cos2θ1x=2\cos^2 \theta - 1

Now get yy in terms of only cosθ\cos \theta. Then think about how you can eliminate the cosθ\cos \theta variable so you have an equation containing only xx and yy.

Ask if you still need help - don't worry if you can't do it since this type of question is new to you.
Reply 15
Original post by King Leonidas
Just fine, as long as I can count that's the main thing:u:

Learning all those equations and symbols just seems mundane, and only a necessity for a career, which would require use of it.

Prepare your angus for this controversial comment:

Spoiler



I was being facetious - of course you don't need A Level maths :smile: GCSE maths is all you need for the vast majority of careers.
Original post by Notnek
I was being facetious - of course you don't need A Level maths :smile: GCSE maths is all you need for the vast majority of careers.

Just stared at your avatar for a minute straight, now my head hurts:frown:
Reply 17
Original post by King Leonidas
Just stared at your avatar for a minute straight, now my head hurts:frown:

Then I recommend having some pills ready if you decide to click on this link.
Original post by Notnek
Then I recommend having some pills ready if you decide to click on this link.

Dude, not cool:colonhash:

Seriously, I think you just gave me Epilepsy.
Reply 19
Original post by Notnek
The second one is what you need since this is only in terms of cosθ\cos \theta. So you have

x=2cos2θ1x=2\cos^2 \theta - 1

Now get yy in terms of only cosθ\cos \theta. Then think about how you can eliminate the cosθ\cos \theta variable so you have an equation containing only xx and yy.

Ask if you still need help - don't worry if you can't do it since this type of question is new to you.


Thank you for breaking this down for me. Could you please check if the solution I reached is correct?

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