How many values of $x$ with $0^\circ \le x < 360^\circ$ satisfy $\sin x = -0.73$?
I know that the sine function is negative in the third and fourth quadrants, so I expect to find two solutions in that interval. I can use a calculator to find the reference angle, which is the angle in the first quadrant that has the same sine value as $x$. To do that, I take the inverse sine of the absolute value of $-0.73$, which gives me $\sin^{-1}(0.73) \approx 47.24^\circ$. This means that $x$ is either $180^\circ$ more or less than this reference angle, depending on which quadrant it is in. So, one solution is $x = 180^\circ + 47.24^\circ \approx 227.24^\circ$, which is in the third quadrant. The other solution is $x = 360^\circ - 47.24^\circ \approx 312.76^\circ$, which is in the fourth quadrant. Therefore, there are two values of $x$ that satisfy the equation in the given interval. 