C3 trig helpWatch

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Thread starter 6 years ago
#1
Well we know that sin2x = 2sinxcosx

What would sin5x be equal to?

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6 years ago
#2
sin5x = sin(3x+2x) or equivalent, then you can use compound angle formula.

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6 years ago
#3
sin5x = sin(2x+3x)...use compound angle formula, for justice!
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Thread starter 6 years ago
#4
And how would I get it into the format of "2sinxcosx"?
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6 years ago
#5
(Original post by Air1337)
And how would I get it into the format of "2sinxcosx"?
you wouldn't, since it does not take that format

Sin3x = Sin(2x+x) = Sin2xCosx + Cos2xSinx = 2Sin^2xCosx + Cos^2xSinx - Sin^x

This can be given in different formats by changing Sin^2x or Cos^2x

Then Sin5x=Sin(3x+2x)
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6 years ago
#6
If you know about De Moivre's Theorem (FP2/FP3- Further Maths), then you could use that to work it out...

if not, then just split it up using the compound angle formulae
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Thread starter 6 years ago
#7
(Original post by TenOfThem)
you wouldn't, since it does not take that format

Sin3x = Sin(2x+x) = Sin2xCosx + Cos2xSinx = 2Sin^2xCosx + Cos^2xSinx - Sin^x

This can be given in different formats by changing Sin^2x or Cos^2x

Then Sin5x=Sin(3x+2x)
So you can only put it into that format if it's an even angle? So what would it be for sin6x for example?
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6 years ago
#8
(Original post by Air1337)
So you can only put it into that format if it's an even angle? So what would it be for sin6x for example?
no

sin(2x) can be written in that format

nothing else
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Thread starter 6 years ago
#9
(Original post by TenOfThem)
no

sin(2x) can be written in that format

nothing else
Hmm alright thanks.
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6 years ago
#10
(Original post by Air1337)
Hmm alright thanks.
But note that sin(6x) = sin(2(3x)) = 2sin3xcos3x
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Thread starter 6 years ago
#11
(Original post by davros)
But note that sin(6x) = sin(2(3x)) = 2sin3xcos3x
Thanks and sin8x = sin(2(4x)) = 2sin4xcos4x?
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6 years ago
#12
for god sake its just 10sin2.5xcos2.5x lol
1
6 years ago
#13
(Original post by TenOfThem)
no

sin(2x) can be written in that format

nothing else
how my heinemen book and teachers told me that you can sin6x into 2sin3xcos3x
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6 years ago
#14
(Original post by yaboy)
how my heinemen book and teachers told me that you can sin6x into 2sin3xcos3x
The OP asked about sin5x and I think TenOfThem was making the point that in general you can't write sin(kx) in the form Asinmxcosnx where k, m and n are all integers.

However, you can always write sin(2nx) = 2sin(nx)cos(nx).
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6 years ago
#15
(Original post by yaboy)
how my heinemen book and teachers told me that you can sin6x into 2sin3xcos3x

well, yes, of course

Sin(2nx) = 2Sin(nx)Cos(nx)

But that is not in the form kSin(x)Cos(x)
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