I am trying to solve 0=1-asin(a) for a, but I have reached a dead end at sin(a) = 1/a. From here I'm not sure what to do.

asin(a)-1=0

asin(a)=1
a=(2k+1/2)π where k=integer
Use the graph of sin(x) to solve for a.

Note:
asin(a) does NOT equal 1/sin(a).
asin(a)=x means sin(x)=a

I think I should restate this, I am trying to solve 0=1-a(sin(a). I didn't mean asin to mean arcsin, it's supposed to be a(sin(a)).

Are you doing Calculus or pre-calculus?

I believe that to solve for
sin(x)=1/x
requires numerical methods, such as Newton's method, or other approximation methods.

You can also plot sin(x) and 1/x and see where they intersect or as approximations.
See:
http://img543.imageshack.us/img543/7304/1338947466.png

To solve the equation 0 = 1 - asin(a) for a, you have made progress by simplifying it to sin(a) = 1/a. However, finding the exact analytic solution for this equation is challenging because there is no algebraic expression for a in terms of elementary functions.

One possible approach to proceed with solving this equation is to use numerical methods, such as iterative techniques or graphing methods, to obtain an approximate solution. These methods can help find a numerical value for a that satisfies the equation sin(a) = 1/a.

Here is a step-by-step explanation of one numerical method called the fixed-point iteration method:

1. Start by rearranging the equation sin(a) = 1/a to the form a = asin(a).

2. Choose an initial guess for a, let's say a₀. It can be any value that you think might be close to the solution.

3. Use the equation aᵢ₊₁ = asin(aᵢ), where "i" denotes the iteration number, to find the next approximation a₁, a₂, a₃, and so on.

4. Repeat step 3 until the values of aᵢ₊₁ become stable, meaning they converge to a single value. This indicates that you have found an approximate solution for a that satisfies the given equation.

Keep in mind that numerical methods provide an approximation, so the accuracy of the solution you obtain will depend on the method used and the number of iterations performed. Additionally, it is essential to verify the solution obtained by substituting it into the original equation and checking if it satisfies it.

If you are working with a specific context or have additional constraints for the equation, please provide more information, and I can try to assist you further.