which is an example x-intercept of the graph of the function y=tan(x-(5pi/6))

Accepted Solution

Answer: x = 5Ο€/6


1) Given function:

[tex]y=tan(x- \frac{5 \pi }{6} )[/tex]

2) x-intercept are the roots of the function, i.e. the solution to y = 0

3) to find when y = 0, you can either solve the equation or look at the graph.

4) Solving the equation you get:

y = 0 β‡’ tan(x - 5Ο€/6) = 0 β‡’ x - 5Ο€/6 = arctan(0)

arctan(0) is the angle whose tangent is zero,so this is 0

β‡’ x - 5Ο€/6 = 0 β‡’ x = 5Ο€/6.

Then, one example of an x-intercept is x = 5Ο€/6, which means that when x = 5Ο€/6, the value of the function is 0.

Since, the tangent function is a periodic function, there are infinite x-intecepts, that is why the questions asks for one example and not all the values.

You can verify by replacing the value x = 5Ο€/6 in the given function:

y = tan (5Ο€/6 - 5Ο€/6) = tan(0) = 0.