# Help integrating sin^2(x-pi/6)

K.QMUL
Hi there everyone,

sin^2(x-pi/6) dx

I have the following integral to solve but am unsure where I should start, I first thought about integrating by parts as I thought you could split it into [Sin(x-pi/6)][Sin(x-pi/6)]. But couldn't seem to figure that out. I was wondering if you could use a trig identity but again am unsure which one.

Any suggestions?

Homework Helper
Gold Member
Dearly Missed
Use the double angle formula. This is a very handy formula to reduce the exponent in a trigfunction appearing in your problem.

Integration by parts works nicely as well, if you are careful with your notation.

K.QMUL
which double angle formula would I use, we still have a Sin^2 to deal with

Homework Helper
Gold Member
Dearly Missed
Well, use the double angle formula in which sin^2 appears on its own, of course.

K.QMUL
Aha, yes, Thanks for the help

K.QMUL
I have completed the question using the double angle formula, could you tell me if you find any errors, as im still unsure whether I have done this right or not.

Thanks

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Saitama
I have completed the question using the double angle formula, could you tell me if you find any errors, as im still unsure whether I have done this right or not.

Thanks

There is a sign error in the end. What is ##\displaystyle \int \cos(x) \, dx##?

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K.QMUL
integrating cos(x) is -sin(x) + c, I took that in consideration as it was 1-cos(x), thus using two negatives = positive, I corrected it to x + 1/2 sin(2x- pi/3).

Does everything look good for this integration? Since I checked on Wolfram Mathematica's on-line integration and the answer they got was

http://integrals.wolfram.com/index.jsp?expr=sin^2(x-pi/6)&random=false

K.QMUL
oh, I realise my mistake, integrating cos(x) = sin(x)

Staff Emeritus
Homework Helper
I have completed the question using the double angle formula, could you tell me if you find any errors, as im still unsure whether I have done this right or not.
You can always check your answer by differentiating it and seeing if you recover the integrand.

K.QMUL
So Ive completed the question, and checked if I get the original answer by differentiating it. And it seems good. HOWEVER, I have one concern; when you use the double angle formula, can I take 'A' as (x - pi/6) in sin^2(x-pi/6) or would I need to split it somehow. Please clear up my confusion.

Staff Emeritus
Homework Helper
What does 'A' represent?

K.QMUL
In terms of the question: sin2

K.QMUL
Sorry, in terms of the formula: sin2A = 0.5[1-cos2A]

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