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anonymous

  • 5 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.

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  1. anonymous
    • 5 years ago
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    The answer is multiples of 90*. Correct?

  2. anonymous
    • 5 years ago
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    Not quite. 0 is a multiple of 90 and tan(0)=0

  3. anonymous
    • 5 years ago
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    I'm having a hard time understanding this question.

  4. anonymous
    • 5 years ago
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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?

  5. anonymous
    • 5 years ago
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    When cos(theta)=(pi/2)

  6. anonymous
    • 5 years ago
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    When else?

  7. anonymous
    • 5 years ago
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    When it is 90*?

  8. anonymous
    • 5 years ago
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    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
    • 5 years ago
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    cot(theta)

  10. anonymous
    • 5 years ago
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    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
    • 5 years ago
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    Thanks for taking the time to explain

  12. anonymous
    • 5 years ago
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    No problem :)

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