conics algebra struggle..... (1 Viewer)

[RideTheLightnin]

hey guys, just struggling with some conics algebra. Its to do with equation of chords for an ellipse, and its on page 89 of <st1:city><st1 ="">Cambridge</st1></st1:city>. Ok I don’t understand how this step:<o =""></o>
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b (sin θ – sin f ) <o =""></o>
a (cos θ – cos f )
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gets to this step:
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b x 2 sin ( θ- f )/2 x cos (θ + f )/2 <o =""></o>
a -2 sin ( θ - f)/2 x sin (θ + f )/2
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thanks, help very much appreciated.


btw "f"s a meant to be that fi symbol, coudlnt find it

 

[Riviet]

It's using two trig identities that aren't in the syllabus but are useful to know:
sinA-sinB=2sin[(A-B)/2].cos[(A+B)/2]
cosA-cosB=-2sin[(A-B)/2].sin[(A+B)/2]
There are also two other similar identities that you can also get expressions of [sinA+sinB, cosA+cosB].

 

[icycloud]

They just used the sum to product formulae.
See here: http://www.mathwords.com/s/sum_to_product_identities.htm

 

[_ShiFTy_]

They are just using the formula:

sin(p) - sin(q) = 2sin[(p-q)/2] . cos[(p+q)/2]

cos(p) - cos(q) = -2sin[(p-q)/2] . sin[(p+q)/2]

You can work these formulas out by mucking around with the basic trig identies:

e.g. sin (a+b) - sin (a-b) = 2sinbcosa

Let a+b=p
Let a-b =q

b = (p-q)/2
a = (p+q)/2


You can either memorise these formulas, or just know how to derive them. You may need to use these formulas in integration
e.g.. Integral of sin(mx)cos(nx)

 

[pLuvia]

It's using two trig identities that aren't in the syllabus but are useful to know:
sinA-sinB=2sin[(A-B)/2].cos[(A+B)/2]
cosA-cosB=-2sin[(A-B)/2].sin[(A+B)/2]
There are also two other similar identities that you can also get expressions of [sinA+sinB, cosA+cosB].

Isn't it in the 4unit course? I heard my teacher say that it was

 

[RideTheLightnin]

oh k thanks guys......after all that it was something i hadnt learnt lol.....i was trying to everything lol.....like midpoint and and all the identities i knew....but cheers thanks guys very helpful

 

[Riviet]

Isn't it in the 4unit course? I heard my teacher say that it was

We should be more familiar to it than the 2/3 uniters.

 

[Raginsheep]

Isn't it in the 4unit course? I heard my teacher say that it was

I don't think it is officially although any maths teacher worth his (meger) wage would at least briefly brush over it. You don't really need to remeber it though.....as long as you know how to derive it you can use the trig expressions that are clearly in the syllabus.

Oh and damn you rivet and pluvia for your similarly coloured avatars.....for a moment I was confused at why riviet was quoting and arguing with himself until I realised it was pluvia....

 

[Mountain.Dew]

for 2/3 U students, usually in the HSC exam, THEY WILL get you to derive the formula as a part of a question, say as part (i). then of course, later parts, (ii) and/or (iii) would involve you applying that formulae.

i think even in the 4U exam they will get you to do this as well. but it is worthwhile having a look at it, and knowing how to derive them, and doing that deriving urself.

 

[Raginsheep]

If you're particularly lucky, they may even give you the formula...