# Solve for Theta

• Jan 11th 2010, 02:28 PM
gwammy
Solve for Theta
Its been a while since I really had to deal with an equation like this, and I might just be missing a simple trig identity. I would really appreciate any help you might be able to give me.

I don't believe I have made any mistakes getting here because I can extrapolate the solution from a graphing calc, and the solution works in my application.

I am trying to solve for Θ in the following equation (I am working in degrees):

ΔL = (π * r * Θ / 45) - (4 * r * sinΘ)
• Jan 11th 2010, 02:46 PM
bigwave
Quote:

Originally Posted by gwammy
Its been a while since I really had to deal with an equation like this, and I might just be missing a simple trig identity. I would really appreciate any help you might be able to give me.

I don't believe I have made any mistakes getting here because I can extrapolate the solution from a graphing calc, and the solution works in my application.

I am trying to solve for Θ in the following equation (I am working in degrees):

ΔL = (π * r * Θ / 45) - (4 * r * sinΘ)

what does the "triangle L" mean

otherwise is this the equation

$
?? = \frac{\pi r \theta}{45^o} - 4 r \sin{\theta}
$

also, mixing degree's with $\pi$ is confusing
• Jan 11th 2010, 03:17 PM
gwammy
The Triangle is a "delta". It signifies a change in that value. In this case, I am working out the change in length of a series of arcs that starts and ends at the same points of a straight line.

Yes, working with degrees when using PI can be confusing, and I could change it, but the CAD program that I am working with works best in degrees, not radians. I apologize for confusing the numbers further.

All of that aside, your equation is correct.
• Jan 12th 2010, 09:26 AM
gwammy
Simplified version
Essentially, after simplifying further, I am just looking to solve for Θ for the following:

X = Θ - sin Θ
• Jan 12th 2010, 10:44 AM
Hello gwammy
Quote:

Originally Posted by gwammy
Essentially, after simplifying further, I am just looking to solve for Θ for the following:

X = Θ - sin Θ

You won't be able to get an exact solution to an equation like this. You'll have to use some sort of numerical method ; e.g. Newton's method. Or if you have access to a spreadsheet (e.g. Excel), then it's very quick to use a 'goal seek' method to find $\theta$ to give a particular value of $x$.