Looking at the image, since the point (-5/13, 12/13) is on a unit circle, that means the x-coordinate is the cosine of angle theta and the y-coordinate is the sine of angle theta.
Since the point is in quadrant II, that means angle theta is between pi/2 and pi (in degrees: 90° and 180°).
Calculating the arc cosine of -5/13, we have:
[tex]\begin{gathered} \cos (\theta)=-\frac{5}{13} \\ \theta=\cos ^{-1}(-\frac{5}{13}) \\ \theta=112.62\degree \end{gathered}[/tex]
Therefore the value of theta is 112.62°.
