Is the function $\frac{1}{\sin x}$
continuous on the interval $\frac{3 \pi}{4} \leq x \leq \frac{5 \pi}{4}$
?

Name: Is the function $\frac{1}{\sin x}$ continuous on the interval $\frac{3 \pi}{4} \leq x \leq \frac{5 \pi}{4}$ ?
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Question

Is the function $\frac{1}{\sin x}$
 continuous on the interval $\frac{3 \pi}{4} \leq x \leq \frac{5 \pi}{4}$
 ?

Quizplus · Accepted Answer

The function $\frac{1}{\sin x}$ is not continuous on the interval $\frac{3 \pi}{4} \leq x \leq \frac{5 \pi}{4}$ because $\sin x = 0$ at $x = \pi$, which is within the given interval, and division by zero is undefined, causing a discontinuity at $x = \pi$.

Is the Function 1sin⁡x\frac{1}{\sin x}sinx1​ Continuous on the Interval 3π4≤x≤5π4\frac{3 \pi}{4} \leq x \leq \frac{5 \pi}{4}43π​≤x≤45π​

Is the Function $\frac{1}{\sin x}$ Continuous on the Interval $\frac{3 \pi}{4} \leq x \leq \frac{5 \pi}{4}$