Can You Solve for Theta in Terms of a Known Expression?

[francisg3]

This is part of a bigger problem, I need to find an expression in terms of θ for the expression below.


1. x=(2r sin⁡θ)/3θ where x=r/2
2. r/2=(2r sin⁡θ)/3θ
3. r=(4r sin⁡θ)/3θ
4. 1=(4 sin⁡θ)/3θ
5. 1/4= sin⁡θ/3θ
6. 3θ/4= sin^-1(θ)

I don't know where to go from there. All I need is an expression in the form of θ= ...


Thanks!

 

[tiny-tim]

hi francisg3!

(try using the X² icon just above the Reply box )

1. x=(2r sin⁡θ)/3θ where x=r/2
2. r/2=(2r sin⁡θ)/3θ
3. r=(4r sin⁡θ)/3θ
4. 1=(4 sin⁡θ)/3θ
5. 1/4= sin⁡θ/3θ
6. 3θ/4= sin^-1(θ)

I don't know where to go from there. All I need is an expression in the form of θ= ...


Thanks!

i'm confused …

6. has sin^-1θ …

were they all supposed to have sin^-1θ ?

anyway, when you have A = sin^-1B,

you can take sin of both sides, giving you sinA = B

 

[HallsofIvy]

However, in general, if you have the unknown both inside a transcendental function, such as sine) and outside it, there is no simple "algebraic" way to solve for it.