Question

Which is an x-intercept of the graph of the function y=cot(3x)

Answer 1

Answer:

x-intercept of the graph of the function $y = \cot(3x)$ is, $(\frac{\pi}{6} \pm \frac{n\pi}{3} , 0)$

Step-by-step explanation:

Given the function: $y = \cot(3x)$                        ......[1]

x-intercept defined as the graph crosses the x-axis.

Substitute value of y = 0 in [1] and solve for x;

$0 = \cot(3x)$ or

$\cot(3x) = 0$

Take the inverse cotangent of both sides of the equation and solve for x;

3x = arccot (0)

We know the exact value of $arc\cot(0) = \frac{\pi}{2}$

then;

$3x = \frac{\pi}{2}$

Divide both sides by 3 we get;

$x = \frac{\pi}{6}$

Since, the cotangent function is positive in the first and third quadrants.

The period of the function $\cot(3x)$ is $\frac{\pi}{3}$ so values will repeat every $\frac{\pi}{3}$  radians in both directions.

we have;

$x =\frac{\pi}{6} \pm \frac{n\pi}{3}$

Therefore, the x-intercept of the graph of the function $y = \cot(3x)$  is ;

$(\frac{\pi}{6} \pm \frac{n\pi}{3} , 0)$  for every integer n;