First you need to find the radius. We know that a circle centered on the origin has the equation
R^2 = x^2 + y^2.
You are given values for an (x,y) point.
Next, consider that you have a triangle bounded by
-- the x-axis
-- the radial line going out to (3,4)
-- the tangent line
Since this is a right triangle, you can find its area.
Then you have the "pie slice" area between the x-axis and the radial line.
Subtract that from the triangle, and what is left is one wing of the darkened area.
Go for it!