Question

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

Answer 1

Let's check

#A

`\\ \tt\hookrightarrow cot(5\pi)/(6)=-√(3)`

• True

#B

`\\ \tt\hookrightarrow cot(7\pi)/(4)=√(3)`

• No not part of graph

#C

`\\ \tt\hookrightarrow cot(4\pi)/(3)=(1)/(√(3))`

• No not part of the graph

Answer 2

`\sf C) \quad \left((4\pi)/(3), √(3)\right)`

Explanation:

Given function:

`y=\cot x \implies y=(1)/(\tan x)`

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

`\textsf{When }\:x=(5 \pi)/(6): \quad y=(1)/(\tan \left((5 \pi)/(6)\right))=(1)/(-(√(3))/(3))=-√(3)`

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

`\textsf{When }\:x=(4 \pi)/(3): \quad y=(1)/(\tan \left((4 \pi)/(3)\right))=(1)/(√(3))=(√(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((4\pi)/(3), √(3)\right)`

(Please see attached graph for proof).