What is the equation for making theta the subject in this scenario?

[questions_uk]

hi. with It = Io sin^2 x (4 x theta) x sin^2 (pi x dn x p / lambda) what would the equation be for making theta the subject? thanks for your input

 

[symbolipoint]

hi. with It = Io sin^2 x (4 x theta) x sin^2 (pi x dn x p /lambda) what would the equation be for making theta the subject? thanks for your input

What are you trying to express? I_t=I_osin²(4$$\theta$$sin²($$\pi$$dnp/$$\lambda$$)

Maybe some of that needs to be amended as
$$\frac{\pi dnp}{\lambda}$$
The typesetting tools available in the Compose for replying are new to me.

I know that did not work, I still have trouble with these typesetting features.

 

[HallsofIvy]

questions_uk, start by "reversing" what is there, just like solving any equation. Everything except $sin^2(4\theta)$ is a constanat so just divide both sides by $Io sin^2(\pi dn p/\lambda$ to get
$$sin^2(4\theta)= \frac{It}{Iosin^2(\pi dn p/\lambda)}$$
Get rid of the "2" by doing the opposite: square root
$$sin(4\theta)= \sqrt{\frac{It}{Iosin^2(\pi dn p/\lambda)}$$
and get rid of the sin by using arcsin:
$$4\theta= arcsin\left(\sqrt{\frac{It}{Iosin^2(\pi dn p/\lambda}\right)$$
Finally, of course, divide both sides by 4.

Since squaring and sine are not "one-to-one" functions, you might need to think about other possible values.

Symbolipoint, use "\", not "/" inside LaTex. And I recommend that you put entire equations in LaTex, not just individual symbols. In the second one here, you had a "tex", "/tex" pair inside another!

 

[questions_uk]

questions_uk, start by "reversing" what is there, just like solving any equation. Everything except $sin^2(4\theta)$ is a constanat so just divide both sides by $Io sin^2(\pi dn p/\lambda$ to get
$$sin^2(4\theta)= \frac{In}{Iosin^2(\pi dn p/\lambda)}$$
Get rid of the "2" by doing the opposite: square root
$$sin(4\theta)= \sqrt{\frac{In}{Iosin^2(\pi dn p/\lambda)}$$
and get rid of the sin by using arcsin:
$$4\theta= arcsin\left(\sqrt{\frac{In}{Iosin^2(\pi dn p/\lambda}\right)$$
Finally, of course, divide both sides by 4.

Since squaring and sine are not "one-to-one" functions, you might need to think about other possible values.

Symbolipoint, use "\", not "/" inside LaTex. And I recommend that you put entire equations in LaTex, not just individual symbols. In the second one here, you had a "tex", "/tex" pair inside another!

hi, thanks for the reply. where did the In bit come from?

 

[HallsofIvy]

Sorry, that was supposed to be your It.

I have gone back and editted to change In to It.

 

[questions_uk]

Thank you for your help.