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1. A curve C has parametric equations:
x=cos A and y=cos 3A where A lies between 0 and π inclusively

Expand cos(2A+A), and hence show that an equation satisfied by all points on C is y=4x³-3x

Really quite stuck on this one.....any help?
2. (Original post by corkskrew)
A curve C has parametric equations:
x=cos A and y=cos 3A where A lies between 0 and π inclusively

Expand cos(2A+A), and hence show that an equation satisfied by all points on C is y=4x³-3x

Really quite stuck on this one.....any help?
cos(2A+A)=cos2AcosA-sin2AsinA
=cosA[2(cosA)^2-1]-sinA[2sinAcosA]
=2(cosA)^3-cosA-2(sinA)^2cosA
=2(cosA)^3-cosA-2[1-(cosA)^2].cosA
=2(cosA)^3-cosA-2cosA+2(cosA)^3
=4(cosA)^3-3cosA

But y=cos(2A+A)=4(cosA)^3-3cosA
But x=cosA
so y=4x³-3x
3. (Original post by corkskrew)
A curve C has parametric equations:
x=cos A and y=cos 3A where A lies between 0 and π inclusively

Expand cos(2A+A), and hence show that an equation satisfied by all points on C is y=4x³-3x

Really quite stuck on this one.....any help?
It's worth learning the 2 identities

Sin3A = 3sinA - 4sin³A
Cos3A = 4cos³A- 3cosA

Here you have to do the expansion, but if you are allowed to avoid it...

Put y=cos 3A and x=cosA in the second of these to get y=4x³-3x

Aitch
Might add, I'm not the mathematician - go a friend round for revision and he came a cropper on a P3 paper
Thanks again.

A

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