Graphical solution to an equation relating tan(x) to a semi semi circle

[Jayman123]

Homework Statement

Using graphical means, determine how many positive roots exist, as a function of a, the the following equation.

Homework Equations

√(a²-x²) = tan(x)

The Attempt at a Solution

I've sketched graphs showing tan(x) and the semi circle overlapping for various radii. Obviously at the radius increases the number of roots increases but I have no idea how to find a relationship between them. Any help would be awesome!

 

[ehild]

What is the domain of sqrt(a²-x²)? How far does it extend along the x axis?
How many tangent curves are there in that interval?

ehild