What is the period of the basic cosecant function $y=\csc \left(x\right)$?

• A. $180°$
• B. $\pi$
• C. $2\pi$
• D. $360°$

Answer: (C)

Verified step by step guidance

1. Recall that the cosecant function, \( y = \csc(x) \), is the reciprocal of the sine function, so \( \csc(x) = \frac{1}{\sin(x)} \).
2. Understand that the period of a trigonometric function is the length of the interval over which the function completes one full cycle and starts repeating.
3. Since \( \csc(x) \) is based on \( \sin(x) \), the period of \( \csc(x) \) is the same as the period of \( \sin(x) \).
4. Recall that the sine function \( \sin(x) \) has a period of \( 2\pi \) radians (or 360 degrees), meaning \( \sin(x + 2\pi) = \sin(x) \) for all \( x \).
5. Therefore, the period of the basic cosecant function \( y = \csc(x) \) is also \( 2\pi \) radians (or 360 degrees).