There are two points on the unit circle where \(\displaystyle cos(s)= -3/5\). On the unit circle, "cos(s)" is the x coordinate of the point (x, y). Since the unit circle has equation \(\displaystyle x^2+ y^2= 1\) if cos(s)= x= -3/5, then \(\displaystyle \frac{9}{25}+ y^2= 1\) so \(\displaystyle y^2= 1- \frac{9}{25}= \frac{16}{25}\) and \(\displaystyle sin(s)= y= \pm \frac{4}{5}\). Now tangent is "sine over cosine" so we have either \(\displaystyle \frac{\frac{4}{5}}{-\frac{3}{5}}= -\frac{4}{3}\) or \(\displaystyle \frac{-\frac{4}{5}}{-\frac{3}{5}}= \frac{4}{3}\). Since we are told that tangent is negative, the first of those is the correct answer.
