which point is not on the graph of y = csc x?\n(\\frac{2\\pi}{3},\\frac{2\\sqrt{3}}{3})\n(\\frac{\\pi}{6},2)\…

Answer:

$\left(\frac{\pi}{3},\frac{\sqrt{3}}{2}\right)$

Explanation:

Step1: Recall the definition of $\csc x$

$\csc x=\frac{1}{\sin x}$

Step2: Check point $\left(\frac{2\pi}{3},\frac{2\sqrt{3}}{3}\right)$

$\sin\left(\frac{2\pi}{3}\right)=\frac{\sqrt{3}}{2}$, $\csc\left(\frac{2\pi}{3}\right)=\frac{1}{\sin\left(\frac{2\pi}{3}\right)}=\frac{2\sqrt{3}}{3}$

Step3: Check point $\left(\frac{\pi}{6},2\right)$

$\sin\left(\frac{\pi}{6}\right)=\frac{1}{2}$, $\csc\left(\frac{\pi}{6}\right)=\frac{1}{\sin\left(\frac{\pi}{6}\right)} = 2$

Step4: Check point $\left(\frac{\pi}{3},\frac{\sqrt{3}}{2}\right)$

$\sin\left(\frac{\pi}{3}\right)=\frac{\sqrt{3}}{2}$, $\csc\left(\frac{\pi}{3}\right)=\frac{1}{\sin\left(\frac{\pi}{3}\right)}=\frac{2\sqrt{3}}{3}\neq\frac{\sqrt{3}}{2}$

Step5: Check point $\left(\frac{3\pi}{4},\sqrt{2}\right)$

$\sin\left(\frac{3\pi}{4}\right)=\frac{\sqrt{2}}{2}$, $\csc\left(\frac{3\pi}{4}\right)=\frac{1}{\sin\left(\frac{3\pi}{4}\right)}=\sqrt{2}$