Solving a Trig Equation

Date: 3/11/96 at 10:24:36
From: Mueen Nawaz
Subject: Trig stuff

Hi.

I have a question. Suppose I know the value for the expression:

(sin (alpha))/(alpha)

That's sine alpha divided by alpha.

How will I find alpha?  Let's assume the value is 1/60. What's 
alpha?

Mueen Nawaz

Date: 7/3/96 at 22:38:57
From: Doctor Jerry
Subject: Re: Trig stuff

To solve sin(x)/x=1/60 for x (or alpha) is not possible if you 
want to do it "exactly."  The equation  2x+3 = 1/60 can be solved 
exactly or analytically or in closed form, but sin(x)/x = 1/60 
can't be solved in this way.  

You may solve it graphically by plotting the function 
f(x)=sin(x)/x-1/60 and noticing the value of x where it crosses 
the x-axis.

Or you can use the bisection method or Newton's method or any one 
of the root finders on a calculator.  I found x to be 
approximately 3.09006 on my calculator.

-Doctor Jerry,  The Math Forum