at which value will the graph of (y = cot x) have a zero?\na. (\frac{pi}{2})\nb. (\frac{pi}{4})\nc…

Explanation:

Step1: Recall the definition of cotangent

The cotangent function is defined as $\cot x=\frac{\cos x}{\sin x}$. A zero of the function occurs when $\cot x = 0$, which means $\frac{\cos x}{\sin x}=0$. For a fraction $\frac{a}{b}$ to be zero, the numerator $a$ must be zero and the denominator $b\neq0$. So we need $\cos x = 0$ and $\sin x\neq0$.

Step2: Evaluate cosine at given angles

• For $x = \frac{\pi}{2}$, $\cos(\frac{\pi}{2})=0$ and $\sin(\frac{\pi}{2}) = 1\neq0$.
• For $x=\frac{\pi}{4}$, $\cos(\frac{\pi}{4})=\frac{\sqrt{2}}{2}\neq0$.
• For $x=\frac{\pi}{3}$, $\cos(\frac{\pi}{3})=\frac{1}{2}\neq0$.

Answer:

A. $\frac{\pi}{2}$