asymptotes on closed interval

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wendywoo

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i need someone to walk me through the steps.
i know how to find asymptotes for a regular function. first is to factor, cancel, then set the denominator equal to zero. thats how i find the x which is the asymptote. but this equation i don't know what to do because i'm dealing with trig.

how many asymptotes does y=3tan(x/4) have on the closed interval [-3pi, 3pi]
 
tan is undefined at \(\displaystyle \frac{\pi}{2}\). So, \(\displaystyle \frac{x}{4}=\pm \frac{\pi}{2}\)

Find x.
 
Nope, that's as simple as this one gets. You must get better acquainted with the tangent function. It is sometimes defined as tan(x) = sin(x) / cos(x) for cos(x) NOT zero. If you know where cos(x) = 0, you find the same solution.
 
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wendywoo said:
i need someone to walk me through the steps.
i know how to find asymptotes for a regular function. first is to factor, cancel, then set the denominator equal to zero. thats how i find the x which is the asymptote. but this equation i don't know what to do because i'm dealing with trig.

how many asymptotes does y=3tan(x/4) have on the closed interval [-3pi, 3pi]
Click to expand...

If you are still confused - plot the function in your graphic calculator - and look.
 
wendywoo said:
why is it undefined at pi/2.
Click to expand...
Is it true that \(\displaystyle \tan(\theta)=\dfrac{\sin(\theta)}{\cos(\theta)}~?\)

Is it true that \(\displaystyle \cos\left(\frac{\pi}{2}\right)=0~?\)

If you answer yes to both, then why do you ask?
 
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