How do you find the vertical, horizontal and slant asymptotes of: $g (θ) = \frac{tan (θ)}{θ}$ $g(theta) = tan(theta)/(theta)$ ?

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Answer 1 · 2017-10-25T18:20:38

See below.

Vertical asymptotes occur at values that make the function undefined. No interval has been specified so I will use:

$- 2 π \leq θ \leq 2 π$ $-2pi<=theta<=2pi$

$tan (θ)$ $tan(theta)$ is undefiled for, $- \frac{3 π}{2} - π, \frac{π}{2}, \frac{3 π}{2}$ $-(3pi)/2 -pi , pi/2 , (3pi)/2$

The function is also undefined for $θ = 0$ $theta = 0$ ( Division by 0 )

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How do you find the vertical, horizontal and slant asymptotes of: g(theta) = tan(theta)/(theta)g(θ)=tan(θ)θ g(theta) = tan(theta)/(theta)?