Questions: Find the exact value of the following expression. cos^(-1)(-(sqrt(3)/2)) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. cos^(-1)(-(sqrt(3)/2))= (Simplify your answer. Type an exact answer, using π as needed. Use integers or fractions for any numbers in the expression.) B. The function is not defined.

To find the exact value of \(\cos^{-1}\left(-\frac{\sqrt{3}}{2}\right)\), we need to determine the angle whose cosine is \(-\frac{\sqrt{3}}{2}\). The cosine function is negative in the second and third quadrants. The reference angle for \(\frac{\sqrt{3}}{2}\) is \(\pi/6\). Therefore, the angle in the second quadrant is \(\pi - \pi/6 = 5\pi/6\).

To find the angle whose cosine is \(-\frac{\sqrt{3}}{2}\), we first identify the reference angle where \(\cos\) is positive, which is \(\frac{\sqrt{3}}{2}\). The reference angle is \(\frac{\pi}{6}\).

The cosine function is negative in the second and third quadrants. Therefore, we need to find the angle in the second quadrant, which is given by: \[ \theta = \pi - \frac{\pi}{6} = \frac{6\pi}{6} - \frac{\pi}{6} = \frac{5\pi}{6} \]

Thus, the exact value of \(\cos^{-1}\left(-\frac{\sqrt{3}}{2}\right)\) is: \[ \boxed{\frac{5\pi}{6}} \]