+5 I was doing my homework and was stuck on a problem for a really long time, and eventually checked the answer key to try and see if I could understand the solution. This is the first part but I still don't understand what it is saying.
For this question, we're going to use our filled in unit circle:
By definition, answers the question "What is the angle between \(-\pi/2\) and \(\pi/2\) with a sine of \(\frac{-\sqrt{3}}{2}\)?" Since the sine is the vertical coordinate of the corresponding terminal point, we see that the only such angle in the interval is \(-\pi/3\) which means that \(\arcsin\left(-\frac{\sqrt{3}}{2}\right)= -\frac{\pi}{3}\)
Can someone explain to me how this works? Because aren't there two intervals where the angle is? Sorry if this doesn't make sense. All help is greatly appreciated.
