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

Which of the following points is not on the graph of the function y = cot x?-example-1
User Matt Small
by
8.1k points

2 Answers

4 votes

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
User Sanatsathyan
by
8.9k points
4 votes

Answer:


\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).

Which of the following points is not on the graph of the function y = cot x?-example-1
User A Spoty Spot
by
8.3k points

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