Math / Trigonometry

QuestionFill in the blank. The period of $y=\csc x$ is $\square$

Studdy Solution

STEP 1

1. The function $y = \csc x$ is the reciprocal of the sine function, i.e., $\csc x = \frac{1}{\sin x}$ .
2. The period of a trigonometric function is the length of the smallest interval over which the function repeats itself.

STEP 2

1. Determine the period of the sine function $\sin x$ .
2. Relate the period of $\csc x$ to the period of $\sin x$ .

STEP 3

The sine function $\sin x$ has a period of $2\pi$ . This means that $\sin(x + 2\pi) = \sin x$ for all $x$ .

STEP 4

Since $\csc x = \frac{1}{\sin x}$ , the period of the cosecant function $\csc x$ is the same as the period of the sine function. Therefore, the period of $\csc x$ is also $2\pi$ .
The period of $y = \csc x$ is $\boxed{2\pi}$ .

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