For what numbers theta is f(theta)=tan(theta) not defined? f(theta)=tan(theta) is not defined for numbers that are (even multiples, odd multiples, multiples) of (45*, 90*, 180*). Select an answer from each set of parentheses.

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For what numbers theta is f(theta)=tan(theta) not defined? f(theta)=tan(theta) is not defined for numbers that are (even multiples, odd multiples, multiples) of (45*, 90*, 180*). Select an answer from each set of parentheses.

Mathematics
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The answer is multiples of 90*. Correct?
Not quite. 0 is a multiple of 90 and tan(0)=0
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Okay, note that \[\tan \theta = \frac{\sin \theta}{\cos \theta}\] Fractions are undefined when their denominator is zero. So when does this occur?
When cos(theta)=(pi/2)
When else?
When it is 90*?
There are an infinite number of points where cos(theta)=0, One of them is 90 degrees (or pi/2), what are the others? There is one more under 2pi, and that should be enough to show you the pattern and give you the answer. Consider what cos looks like on the unit circle.
cot(theta)
Okay, cos(theta)=0 when theta is \[\cdots,-\frac{3\pi}{2},-\frac{\pi}{2},\frac{\pi}{2},\frac{3\pi}{2}, \cdots\] or \[\cdots, -270, -90, 90, 270, \cdots\] So the answer is odd multiples of 90 degrees.
Thanks for taking the time to explain
No problem :)

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