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Question

Find four values for which each function is undefined.
f(θ)=tanθf(\theta)=\tan \theta

Solution

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The values that makes the function undefined is the values of the asymptotes. So for the given function:

f(θ)=tanθf(\theta) = \tan \theta

Because b=1b = 1, the function will be undefined at:

θ=π2b+nπb=π2+nπ\theta = \frac{\pi}{2|b|} + \frac{n\pi}{|b|} = \frac{\pi}{2} + n\pi

Then, the first for values will be at n=1, n=2, n=3n = 1,\ n = 2,\ n = 3 and n=4n = 4, which are:

θ=π2 ,  θ=3π2 ,  θ=5π2,  and   θ=7π2\theta = \frac{\pi}{2}\ ,\ \ \theta = \frac{3\pi}{2}\ ,\ \ \theta = \frac{5\pi}{2} ,\ \ \text{and}\ \ \ \theta = \frac{7\pi}{2}

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