Question

If sin(Θ)=x^2, what is sin(2Θ) in terms of x?

Answer 1

do you know how to express sin(2a) in terms of sin(a) and cos(a)?

Answer 2

um, sin(2a)=2sin(a)cos(a), right?

Answer 3

perfect - now you just need to express cos(a) in terms of sin(a).
do you know how to do that?

Answer 4

Is it cos(a)=sin(a+π/2)? cuz that's where i'm stuck.

Answer 5

no - use the following identity:\[\sin^2(a)+\cos^2(a)=1\]

Answer 6

the rest should be simple

Answer 7

Oh...OK. So it is 2x^2 sqrt(1-x^4)

Answer 8

that looks right to me

Answer 9

Thanks for your help!

Answer 10

yw :)

Answer 11

note in some cases you will need \[-2x^2\sqrt{1-x^4}\]

Answer 12

yes indeed - @Zarkon spotted something we both failed to spot:\[\cos(a)=\pm\sqrt{1-\sin^2(a)}\]