## anonymous 4 years ago 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.

1. anonymous

The answer is multiples of 90*. Correct?

2. anonymous

Not quite. 0 is a multiple of 90 and tan(0)=0

3. anonymous

I'm having a hard time understanding this question.

4. anonymous

Okay, note that $\tan \theta = \frac{\sin \theta}{\cos \theta}$ Fractions are undefined when their denominator is zero. So when does this occur?

5. anonymous

When cos(theta)=(pi/2)

6. anonymous

When else?

7. anonymous

When it is 90*?

8. anonymous

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.

9. anonymous

cot(theta)

10. anonymous

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.

11. anonymous

Thanks for taking the time to explain

12. anonymous

No problem :)