# Centroid of Circuar Sector

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!

## Answers and Replies

tiny-tim
Science Advisor
Homework Helper
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
Science Advisor
Homework Helper
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.