Answer:
x-intercept of the graph of the function [tex]y = \cot(3x)[/tex] is, [tex](\frac{\pi}{6} \pm \frac{n\pi}{3} , 0)[/tex]
Step-by-step explanation:
Given the function: [tex]y = \cot(3x)[/tex] ......[1]
x-intercept defined as the graph crosses the x-axis.
Substitute value of y = 0 in [1] and solve for x;
[tex]0 = \cot(3x)[/tex] or
[tex]\cot(3x) = 0[/tex]
Take the inverse cotangent of both sides of the equation and solve for x;
3x = arccot (0)
We know the exact value of [tex]arc\cot(0) = \frac{\pi}{2}[/tex]
then;
[tex]3x = \frac{\pi}{2}[/tex]
Divide both sides by 3 we get;
[tex]x = \frac{\pi}{6}[/tex]
Since, the cotangent function is positive in the first and third quadrants.
The period of the function [tex]\cot(3x)[/tex] is [tex]\frac{\pi}{3}[/tex] so values will repeat every [tex]\frac{\pi}{3}[/tex] radians in both directions.
we have;
[tex]x =\frac{\pi}{6} \pm \frac{n\pi}{3}[/tex]
Therefore, the x-intercept of the graph of the function [tex]y = \cot(3x)[/tex] is ;
[tex](\frac{\pi}{6} \pm \frac{n\pi}{3} , 0)[/tex] for every integer n;
The x-intercept of the graph of the function y = cot(3x) is [tex]x = \frac{\pi}6[/tex]
The graph of the function is given as:
y = cot(3x)
To determine the x-intercept of the graph, we set the graph to 0.
So, we have:
cot(3x) = 0
Take the arccot of both sides
3x = arccot(0)
Evaluate the arccot of 0
[tex]3x = \frac{\pi}2[/tex]
Divide both sides by 3
[tex]x = \frac{\pi}6[/tex]
Hence, the x-intercept of the graph of the function y = cot(3x) is [tex]x = \frac{\pi}6[/tex]
Read more about x-intercepts at:
https://brainly.com/question/3951754
