Select your answer (4 out of 6) Simplify \( \cot \left(\frac{3 \pi}{2}\right) \). \( -\infty \) \( -1 \) 0 1 \( \infty \)

To simplify \( \cot \left(\frac{3 \pi}{2}\right) \), we start by recalling what cotangent is. Cotangent is defined as \( \cot(x) = \frac{\cos(x)}{\sin(x)} \). At the angle \( \frac{3 \pi}{2} \) (or 270°), the coordinates on the unit circle are (0, -1). Thus, \( \sin\left(\frac{3 \pi}{2}\right) = -1 \) and \( \cos\left(\frac{3 \pi}{2}\right) = 0 \). Using the cotangent definition: \[ \cot\left(\frac{3 \pi}{2}\right) = \frac{\cos\left(\frac{3 \pi}{2}\right)}{\sin\left(\frac{3 \pi}{2}\right)} = \frac{0}{-1} = 0 \] So, the correct answer is \( 0 \).