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Just found this forum and wow it's good

Probably really simple how to do this but I'm stuck on what to do:-

By expressing sin3A as sin(2A + A), find an expression for sin3A in terms of sin A

Any help would be greatly appreciated

Thanks

Probably really simple how to do this but I'm stuck on what to do:-

By expressing sin3A as sin(2A + A), find an expression for sin3A in terms of sin A

Any help would be greatly appreciated

Thanks

sin(x+y)=sinxcosy+sinycosx

Let x=2A and y=A

=>sin(3A)=sin(2A+A)=sin2AcosA+sinAcos2A

* sin2A=2sinAcosA cos2A=(1-2sin²A)

=>sin(3A)=(2sinAcosA)cosA+sinA(1-2sin²A)

=>sin(3A)=2sinAcos²A+sinA-2sin³A

* cos²A=(1-sin²A)

=>sin(3A)=2sinA(1-sin²A)+sinA-2sin³A

=>sin(3A)=2sinA-2sin³A+sinA-2sin³A

=>sin(3A)=3sinA-4sin³A

=>sin(3A)=sinA(3-4sin²A)

Newton.

Let x=2A and y=A

=>sin(3A)=sin(2A+A)=sin2AcosA+sinAcos2A

* sin2A=2sinAcosA cos2A=(1-2sin²A)

=>sin(3A)=(2sinAcosA)cosA+sinA(1-2sin²A)

=>sin(3A)=2sinAcos²A+sinA-2sin³A

* cos²A=(1-sin²A)

=>sin(3A)=2sinA(1-sin²A)+sinA-2sin³A

=>sin(3A)=2sinA-2sin³A+sinA-2sin³A

=>sin(3A)=3sinA-4sin³A

=>sin(3A)=sinA(3-4sin²A)

Newton.

needmathshelp

Just found this forum and wow it's good

Probably really simple how to do this but I'm stuck on what to do:-

By expressing sin3A as sin(2A + A), find an expression for sin3A in terms of sin A

Any help would be greatly appreciated

Thanks

Probably really simple how to do this but I'm stuck on what to do:-

By expressing sin3A as sin(2A + A), find an expression for sin3A in terms of sin A

Any help would be greatly appreciated

Thanks

sin(2A+A)=sin2AcosA+sinacos2a

sin(2A+A)=2sinAcosAcosA+sinA(1-2 (sinA)^2)

sin(2a+a)=2 sinA( 1- (sinA)^2))+inA - 2 (sinA)~3

etc...now juat do a little tidying up......

mrm.

needmathshelp

Just found this forum and wow it's good

Probably really simple how to do this but I'm stuck on what to do:-

By expressing sin3A as sin(2A + A), find an expression for sin3A in terms of sin A

Any help would be greatly appreciated

Thanks

Probably really simple how to do this but I'm stuck on what to do:-

By expressing sin3A as sin(2A + A), find an expression for sin3A in terms of sin A

Any help would be greatly appreciated

Thanks

You have a standard formula:

sin(A+B) = sinAcosB + cosAsinB

Substitute

sin(2A+A)=sin2AcosA+cos2AsinA

Sin(2A) = 2sinAcosA

Cos(2A) = 1-2sin

So, we have

2sinAcosAcosA + (1-2sin

= 2sinA(1-sin

= 2sinA - 2sin

= 3sinA - 4sin

= sinA (3 - 4sin

Newton

Why did you answer after I and Mrm. have already answered it before?

Newton.

Newton.

I didn't, I was busy typing, got distracted by the phone and completed my post - by which time two people have already answered, and within a minute I've got you jumping on my back. Marvellous.

Wow cheers guys, it's all clear now

And thanks for not making fun of me cause i didn't get it where as you probably found it easy.

And thanks for not making fun of me cause i didn't get it where as you probably found it easy.

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- A Level Trig Help
- what are all the trig formulae i need to remember ?
- A-level Edexcel Maths - Proofs
- How to find the intersection of this complex graph
- trig
- Linear Transformations Edexcel
- A level math... help
- Struggling with Year 2 pure maths
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- Maths A level - Trignometric proof
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- AS Further Maths May 17th 2024 Further Pure 1 and 2
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