# Thread: Expressing Sin(2p) in terms of x

1. ## Expressing Sin(2p) in terms of x

Hi,

If x = 2sin(p)

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

Thanks

2. 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.

3. 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)]
----------

(sorry mr. fantastic, didn't see you already explained it to him)

4. Thanks

5. 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

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