Question

evaluate the following trigonometric function at the quadrantal angle, or state that the expression is undefined. cot\\(\frac{\pi}{2}\\) select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. cot\\(\frac{\pi}{2}=\\) b. cot\\(\frac{\pi}{2}\\) is undefined.

Explanation:

Step1: Recall the definition of cotangent

The cotangent function is defined as \(\cot\theta=\frac{\cos\theta}{\sin\theta}\).

Step2: Find \(\cos\frac{\pi}{2}\) and \(\sin\frac{\pi}{2}\)

We know from the unit circle that \(\cos\frac{\pi}{2} = 0\) and \(\sin\frac{\pi}{2}=1\).

Step3: Substitute into the cotangent formula

Substitute \(\theta = \frac{\pi}{2}\) into \(\cot\theta=\frac{\cos\theta}{\sin\theta}\), we get \(\cot\frac{\pi}{2}=\frac{\cos\frac{\pi}{2}}{\sin\frac{\pi}{2}}=\frac{0}{1}\).

Step4: Evaluate the fraction

\(\frac{0}{1}=0\).

Answer:

A. \(\cot\frac{\pi}{2}=\boxed{0}\)