Question

Which of the following points is not on the graph of the function y = cot x?

Answer 1

Answer:

$\sf C) \quad \left(\dfrac{4\pi}{3}, \sqrt{3}\right)$

Step-by-step explanation:

Given function:

$y=\cot x \implies y=\dfrac{1}{\tan x}$

Substitute the x-values of the given coordinates into the given function:

$\textsf{When }\:x=\dfrac{5 \pi}{6}: \quad y=\dfrac{1}{\tan \left(\dfrac{5 \pi}{6}\right)}=\dfrac{1}{-\dfrac{\sqrt{3}}{3}}=-\sqrt{3}$

$\textsf{When }\:x=\dfrac{7 \pi}{4}: \quad y=\dfrac{1}{\tan \left(\dfrac{7 \pi}{4}\right)}=\dfrac{1}{-1}=-1$

$\textsf{When }\:x=\dfrac{4 \pi}{3}: \quad y=\dfrac{1}{\tan \left(\dfrac{4 \pi}{3}\right)}=\dfrac{1}{\sqrt{3}}=\dfrac{\sqrt{3}}{3}$

Comparing the y-values of the given coordinates, we can clearly see that point that is not on the graph of the function is:

$\sf \left(\dfrac{4\pi}{3}, \sqrt{3}\right)$

(Please see attached graph for proof).

Answer 2

Let's check

#A

$\\ \tt\hookrightarrow cot\dfrac{5\pi}{6}=-\sqrt{3}$

• True

#B

$\\ \tt\hookrightarrow cot\dfrac{7\pi}{4}=\sqrt{3}$

• No not part of graph

#C

$\\ \tt\hookrightarrow cot\dfrac{4\pi}{3}=\dfrac{1}{\sqrt{3}}$

• No not part of the graph