0
$\begingroup$

Locate the discontinuities of the function.

$$f(x) = \ln(\tan(x)^2)$$

Question is looking for a, $x =$ value.

  • 1
    I smell unattempted homework. Please show what you've done to try to solve this exercise. – 2017-02-10
  • 0
    I'm not the best when it comes to dealing with trigonometry functions. I posted this because I know from the responses I would get an idea on how to proceed. A question, not a homework page. @SirJony – 2017-02-10

3 Answers 3

2

Hint: Where is $\tan x$ defined? You will not have to worry about it being negative since it has been kindly squared. When is it zero?

  • 0
    so I would say tan x is defined between intervals, [-1,1]. @qbert – 2017-02-10
  • 0
    @AlexanderJohn while true, you can do a little better than that – 2017-02-10
  • 0
    It is 0 at $\pi$, $0$, 2$\pi$. – 2017-02-10
1

Begin by analyzing the domain of some functions...

What's the domain of $\tan x$?

$x \neq \frac{\pi}{2} + \pi n$ where $n$ is an integer

What's the domain of $\ln x$?

x > 0

What's the domain of $\tan ^2 x$?

same as the domain of $\tan x$

Now look at the ranges of some functions...

What's the range of $\tan x$?

all real numbers (i.e. $(-\infty, \infty)$)

What's the range of $\tan^2 x$?

all non-negative numbers (i.e. $[0, \infty)$)

Now, put it all together.

0

Hint: $\tan x = \frac{\sin x}{\cos x}$.