The graphical solution to an equation relating tan(x) to a semi circle is achieved by plotting the equation on a graph and finding the points of intersection between the curve and the semi circle.
Tan(x) is the ratio of the length of the opposite side to the adjacent side in a right triangle, and in a semi circle, this ratio represents the slope of the tangent line at any given point on the semi circle.
The graph of tan(x) in a semi circle is restricted to only the first and fourth quadrants, as the opposite and adjacent sides must always be positive in a semi circle. This results in a graph with a half-wave pattern, as opposed to the full-wave pattern of a regular tan(x) graph.
Yes, it is possible for a graphical solution to have multiple solutions, as there can be multiple points of intersection between the curve and the semi circle. These solutions can also be found algebraically by solving the equation for x.
One limitation is that the graphical solution only provides an approximate solution, as it relies on the accuracy of the graph and the precision of the plotting. Additionally, the graphical solution may not work for more complex equations involving multiple trigonometric functions.