c4 parametric (please look at attachment/pic..))

Hi,

I have put together a few questions which I struggled to do and would greatly appreciate if someone could help me out (even if you can help me out with one of the questions and not all 4, it would be great!). If you can explain the answer to me as well as do it, itd be even better!

Question 6 - I couldnt get the whole question
Question 7 - I could do part i and part ii. Part iii was where I got stuck as I didnt even understand what the question was asking!
Question 8 - I got all parts but part iv.
Question 9 - I got part i no problem. I just about got part ii by look at the answers (if someone could further explain the answer to me itd be good) and part iii I didnt understand.

Please help people!

(If you want me to post the answers I can :smile:

)

Thanks a lottt!!

PS - As you can see from my previous posts, I like to pay people back for their help :smile:

parametric qu.JPG77.6KB

Reply 1

limetang

Okay for question 6 you need to firstly differentiate both x and y with respect to x then turn that into an equation for dy/dx. You then need to put the values of your domain into the equation for gradient to show it can't be greater than 6.

For the second part you basically need to rearange the equation to get Cos^2 = something to do with x and sin^2= something to do with y (not sure which is sin and which is cos) then add both the x terms and the y terms together to equal one then rearange.

For the final part just scetch a quadratic graph.

Reply 2

freedomhunter

Original post by limetang

Thanks limetang. I keep getting the wrong answer for part i (i must be differentiating incorrectly!) and sorry, but im still confused about part ii :ashamed2:

Reply 3

limetang

Original post by freedomhunter

Thanks limetang. I keep getting the wrong answer for part i (i must be differentiating incorrectly!) and sorry, but im still confused about part ii :ashamed2:

Okay for part two (admitadely I haven't done all the working yet) what I think you should do involves using your knowledge of trig to get yourself a cartesian equation.

Firstly you know the identity Sin^2 + Cos^2 =1
So what you firstly need to do is arrange your two parametric equations so you have Sin^2 and Cos^2 equalling expressions involving x and y. So because you know the identity Sin^2 + Cos^2 =1 those two expressions added together will equal one.

Heres a fairly simple example.

Sint=x and Cost=y
Therefore Sin^2 t =x^2 and Cos^2 t= y^2
So because Sin^2 + Cos^2 =1
substituting in your values for Sin^2 and Cos^2 you get x^2 + y^2 =1

Okay:

Here's my solution for part ii (if this helps)

x=cost and y= 3+2cos2t

this means that (using double angle formulae)

y= 3+ 2(Cos^2t - Sin^2 t)
(and using Sin^2 + Cos^2 =1)
y=3+2(2Cos^2t -1)

x=Cost
therefrore Cos^2t=x^2

So

y=3 + 2(2x^2 -1)
y=3 +4x^2 -2
y=4x^2 +1

c4 parametric (please look at attachment/pic..))

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