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maths ocr trig question - really struggling

http://www.mei.org.uk/files/papers/c409jn_gegd.pdf

6ii

i got the bit where it says sec^2, but i dont understand the integration, can someone give me a step by step
Reply 1
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C-rated
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Well you have the thing you found the partial fractions for, but it's squared
So it becomes R^2 x cos(Theta-alpha)^2
So it's asking for you to integrate 1/R^2 x sec(theta-alpha) which will become 1/R^2 x the integration
The integration will be tan(theta-alpha) since you're letting (theta-alpha) be equal to x
Since you're treating the (theta-alpha) as a singular value, it won't have an effect on the integration

At this point, you substitute the values into theta so you end up with the answer shown

edit: I should also mention that quite a lot of the integrations/differentiations are in the formula book, so you don't usually have to worry about them, just remember the ones that aren't in there
(edited 7 years ago)
Original post by liverpool2044
http://www.mei.org.uk/files/papers/c409jn_gegd.pdf

6ii

i got the bit where it says sec^2, but i dont understand the integration, can someone give me a step by step


(cosx + sqrt(3)sinx)^2 = (cosx)^2 (1+sqrt(3)tanx))^2 ,so I hope you can see what to do.
Original post by C-rated
Well you have the thing you found the partial fractions for, but it's squared
So it becomes R^2 x cos(Theta-alpha)^2
So it's asking for you to integrate 1/R^2 x sec(theta-alpha) which will become 1/R^2 x the integration
The integration will be tan(theta-alpha) since you're letting (theta-alpha) be equal to x
Since you're treating the (theta-alpha) as a singular value, it won't have an effect on the integration

At this point, you substitute the values into theta so you end up with the answer shown


thank you, why is it 1/the answer to previous though?
Reply 4
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Hjyu1
2
image.jpgI rushed it so it's messy but using the parts before u should get this
Reply 5
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Hjyu1
2
Original post by liverpool2044
thank you, why is it 1/the answer to previous though?


You work out the equivalent of cos theta + sqrt3 sin theta in the first part and that's what's on the bottom of the integral
Reply 6
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Original post by liverpool2044
thank you, why is it 1/the answer to previous though?


They asked you to change it into a different form so now they're asking for you to apply that different form to another question to get the answer

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