Air1337
Badges: 0
Rep:
?
#1
Report Thread starter 6 years ago
#1
Well we know that sin2x = 2sinxcosx

What would sin5x be equal to?

Thanks in advance.
0
reply
tommyth94
Badges: 5
Rep:
?
#2
Report 6 years ago
#2
sin5x = sin(3x+2x) or equivalent, then you can use compound angle formula.


Posted from TSR Mobile
0
reply
boromir9111
Badges: 15
Rep:
?
#3
Report 6 years ago
#3
sin5x = sin(2x+3x)...use compound angle formula, for justice!
0
reply
Air1337
Badges: 0
Rep:
?
#4
Report Thread starter 6 years ago
#4
And how would I get it into the format of "2sinxcosx"?
0
reply
TenOfThem
Badges: 16
Rep:
?
#5
Report 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)
0
reply
LeeMrLee
Badges: 0
Rep:
?
#6
Report 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
0
reply
Air1337
Badges: 0
Rep:
?
#7
Report 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?
0
reply
TenOfThem
Badges: 16
Rep:
?
#8
Report 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
0
reply
Air1337
Badges: 0
Rep:
?
#9
Report Thread starter 6 years ago
#9
(Original post by TenOfThem)
no

sin(2x) can be written in that format

nothing else
Hmm alright thanks.
0
reply
davros
  • Study Helper
Badges: 16
Rep:
?
#10
Report 6 years ago
#10
(Original post by Air1337)
Hmm alright thanks.
But note that sin(6x) = sin(2(3x)) = 2sin3xcos3x
0
reply
Air1337
Badges: 0
Rep:
?
#11
Report 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?
0
reply
yaboy
Badges: 0
Rep:
?
#12
Report 6 years ago
#12
for god sake its just 10sin2.5xcos2.5x lol
1
reply
yaboy
Badges: 0
Rep:
?
#13
Report 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
0
reply
davros
  • Study Helper
Badges: 16
Rep:
?
#14
Report 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).
0
reply
TenOfThem
Badges: 16
Rep:
?
#15
Report 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)
0
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Back
to top
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

University open days

  • University of Bristol
    Undergraduate Open Afternoon Undergraduate
    Wed, 23 Oct '19
  • University of Exeter
    Undergraduate Open Day - Penryn Campus Undergraduate
    Wed, 23 Oct '19
  • University of Nottingham
    Mini Open Day Undergraduate
    Wed, 23 Oct '19

Have you made up your mind on your five uni choices?

Yes I know where I'm applying (152)
59.61%
No I haven't decided yet (58)
22.75%
Yes but I might change my mind (45)
17.65%

Watched Threads

View All