Hi,
If x = 2sin(p)
How do we express sin(2p) in terms of x only?
Thanks
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