I need to solve for x, where x is between -pi/2 and pi/2.
sin(x)=-1/sqrt(2) Anyone know how ?
+1904 \(sin(x)=-\frac{1}{\sqrt{2}}\)
\({sin}^{-1}(sin(x))={sin}^{-1}(-\frac{1}{\sqrt{2}})\)
\(x=-\frac{\pi}{4}\)
That is how you do it with a calculator. To get to the answer without using a calculator, looking at the unit circle, what point on the unit circle between \(-\frac{\pi}{2}\) and \(\frac{\pi}{2}\) is the y value equal to \(-\frac{1}{\sqrt{2}}?\) The point on the unit circle is actually a point that is easily memorized.
