Question

what is the period of the function y = cot x? ?π

Explanation:

Step1: Recall the period of cotangent function

The cotangent function \( y = \cot x \) is defined as \( \cot x=\frac{\cos x}{\sin x} \). The sine function \( \sin x \) has a period of \( 2\pi \), but the cotangent function repeats its values after an interval of \( \pi \) because \( \cot(x + \pi)=\frac{\cos(x + \pi)}{\sin(x + \pi)}=\frac{-\cos x}{-\sin x}=\frac{\cos x}{\sin x}=\cot x \). So the period of \( y = \cot x \) is \( \pi \), which means the coefficient of \( \pi \) is 1.

Answer:

1