How do you find the vertical, horizontal or slant asymptotes for $y = cot (\frac{x}{2})$ $y= cot (x/2)$ ?

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Answer 1 · 2017-08-28T18:02:09

You know that $cot (θ) = \frac{1}{tan (θ)} = \frac{cos (θ)}{sin (θ)}$ $cot(theta) = 1/tan(theta) = cos(theta)/sin(theta)$

and you know that this will be undefined wherever the value of the denominator is zero - because you can't divide by zero.

$sin (θ) = 0$ $sin(theta) = 0$ when $theta = 0,pi,2pi,3pi...$

so, if $x/2 = theta$ , then, we have a vertical asymptote when

$x/2 = 0,pi,2pi,3pi...$

multiply the left side (and every item in the sequence on the right side) by 2 gives us:

$x = 0, 2pi, 4pi, 6pi...$

How do you find the vertical, horizontal or slant asymptotes for y= cot (x/2)y=cot(x2)y= cot (x/2)?