rewrite (sin(2x)^2 in terms of cos(x)

[nicole_]

rewrite (sin(2x))^2 in terms of cos(x)

I need to rewrite (sin(2x))^2 in terms of cos(x)
(sin(2x))^2 = A(cos(x)^4+B(cos(x))^3+C(cos(x))^2+D(cos(x))+E
and find A,B,C,D,E=?

 

[stapel]

I need to rewrite (sin(2x)^2 in terms of cos(x)
(sin(2x))^2 = A(cos(x)^4+B(cos(x))^3+C(cos(x))^2+D(cos(x))+E
and find A,B,C,D,E=?

You're missing a close-paren. Is your original expression meant to be either of the following?

. . . . .\(\displaystyle \Big(\sin(2x)\Big)^2\)

. . . . .\(\displaystyle \sin\Big((2x)^2\Big)\)

When you reply, please include a clear listing of your thoughts and efforts so far. Thank you!

 

[nicole_]

You're missing a close-paren. Is your original expression meant to be either of the following?

. . . . .\(\displaystyle \Big(\sin(2x)\Big)^2\)

. . . . .\(\displaystyle \sin\Big((2x)^2\Big)\)

When you reply, please include a clear listing of your thoughts and efforts so far. Thank you!

It is the first one. I really have no idea how to solve it that the reason why I am asking here.

 

[stapel]

It is the first one.

. . . . .\(\displaystyle \Big(\sin(2x)\Big)^2\)

I really have no idea how to solve it that the reason why I am asking here.

You may not be able to discern all of the steps to the final form, just by looking. But that doesn't mean you can't try stuff.

You've been given the square of a sine, and have been asked to find something in cosines. Since squared sines and cosines are related by an identity, why not try applying that identity first. (here)

Then note that you're asked to find something in cosines of x, not of 2x, but that you've got an identity relating sines of 2x to sines and cosines, so... where does that lead?

If you get stuck, please reply showing all of your thoughts and efforts so far, and we'll be glad to try to provide more hints and helps you get you going again. Thank you!

 

[Deleted member 4993]

I need to rewrite (sin(2x))^2 in terms of cos(x)
(sin(2x))^2 = A(cos(x)^4+B(cos(x))^3+C(cos(x))^2+D(cos(x))+E
and find A,B,C,D,E=?

Hint:

sin(2x) = 2 * sin(x) * cos(x)

 

[pka]

I need to rewrite (sin(2x))^2 in terms of cos(x)

\(\displaystyle \left(\sin(t)\right)^2=1-\left(\cos(t)\right)^2\)

\(\displaystyle \begin{align*}\left(\sin(2x)\right)^2&=1-\left(\cos(2x)\right)^2 \\&= 1-\left(2\cos^2(x)-1\right)^2 \\&= 1-\left(4\cos^4(x)-4\cos(x)+1\right)\end{align*}\)

 

[soroban]

\(\displaystyle \text{Write }[\sin(2x)]^2\text{ in terms of }\cos(x).\)

\(\displaystyle \begin{array}{ccc}
\sin(2x) &=& 2\sin x\cos x \\
& = & 2\sqrt{1-\cos^2x}\cdot\cos x \\ \\

[\sin(2x)]^2 &=& 4(1-\cos^2x)\cos^2 x

\end{array}\)

 

[hoosie]

Express sin^2(2x) in terms of cosx

Express sin^2(2x) in terms of cosx
sin^2(2x) = Acos^4(x) + Bcos^3(x) + Ccos^2(x) + Dcosx + E
and find A,B,C,D,E=?


See if you can fill in the boxes to answer the question:


sin2x = sinxcosx
(Sin2x)^2 = (sinxcosx)^2
= sin^2(x)cos^2(x)
= [- cos^(x)]cos^2(x)
= cos^2(x) - cos^4(x)
= cos^4(x) + cos^3(x) + cos^2(x) + cos(x) +
= Acos^4(x) + Bcos^3(x) + Ccos^2(x) + Dcosx + E
where A = , B = , C = , D = , E =