Hi,

If x = 2sin(p)

How do we express sin(2p) in terms of x only?

Thanks

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- Jan 27th 2009, 11:33 AMalgorithmExpressing Sin(2p) in terms of x
Hi,

If x = 2sin(p)

How do we express sin(2p) in terms of x only?

Thanks - Jan 27th 2009, 11:43 AMmr fantastic
- Jan 27th 2009, 01:04 PMmetlx
- Jan 27th 2009, 02:21 PMalgorithm
Thanks

- Jan 28th 2009, 01:49 AMDavid24
hey mate,

x = 2sin(p) --> sin(p) = x/2

Trig Identity,

sin(2p) = 2sin(p)cos(p) = 2 (x/2) cos(p) = xcos(p)

note cos(p) = sqrt(1-sin^2(p)) = sqrt( 1 - (x/2)^2 ) = sqrt(1 - x^2/4) = sqrt( (4 - x^2)/4)

= sqrt(4-x^2)/2

Hence,

sin(2p) = xcos(p) = x (sqrt(4-x^2)/2) = (x/2)sqrt(4-x^2)

Hope this helps,

David