Last Updated 10/28/2022

Sage Essentials
Section 4: Solving Equations

The find_root and roots command

Example 1

Sometimes, the solve command may fail to find all the solutions of an equation. For example, let use try to find the solutions of $\sin x=\frac{1}{2}$ .

Note that only the solution in the first quadrant is found, namely $\frac{\pi }{6}$  or 0.523598775598299.

To locate other solutions, we can use the find_root command.  The find_root command looks for a solution of an equation in a particular interval.

Let us locate a solution of $\sin x=\frac{1}{2}$  on each of the intervals  $\left[0,\frac{\pi }{2}\right]$ and $\left[\frac{\pi }{2},\pi \right]$ .

Try this!

What happen if we try to look for a solution of $\sin x=\frac{1}{2}$ on $\left[\pi ,2\pi \right]$ .