# How do you locate the discontinuities of the function #y = ln(tan(x)2)#?

##### 1 Answer

Assuming this says

Recall that

Also recall that **vertical asymptote** at **is ZERO every integer**

The first thing to look at is **where the ln function has discontinuities.** The natural log function looks at the value in parentheses and evaluates the power to which e, Euler's number, must be raised to be equal to the value in the parentheses. For example:

From this example, it becomes clear that we will have a problem if we take the natural log of 0. What power could e be raised to to make it 0? The answer is a discontinuity, in this case the discontinuity is negative infinity. Since there is a discontinuity in the ln function at

As a result, this has **discontinuities if**

#x = pm(npi)/2# --- this covers the case of#pm npi# as well as#pm (npi)/2# , as we want#pm pi/2, pm pi, pm (3pi)/2# , etc.

#n in ZZ# .