# Expressing Sin(2p) in terms of x

• Jan 27th 2009, 11:33 AM
algorithm
Expressing 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 AM
mr fantastic
Quote:

Originally Posted by algorithm
Hi,

If x = 2sin(p)

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

Thanks

sin (2p) = 2 sin p cos p.

sin p = x/2. Use the Pythagorean Identity to get cos p from sin p = x/2.
• Jan 27th 2009, 01:04 PM
metlx
Quote:

Originally Posted by algorithm
Hi,

If x = 2sin(p)

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

Thanks

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

sin(2p) = x * cos(p)
x = [sin(2p) / cos(p)]
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(sorry mr. fantastic, didn't see you already explained it to him)
• Jan 27th 2009, 02:21 PM
algorithm
Thanks
• Jan 28th 2009, 01:49 AM
David24
Quote:

Originally Posted by algorithm
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