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Math Help - reciprocal functions question

  1. #1
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    reciprocal functions question

    this question was given on a practice test

    y = sec(x)csc(x)tan(x) Determine if there are any vertical asymptotes or holes

    The answer given was
    Y = sin(x)/[cos(x)sin(x)] = 1/cos(x)
    Therefore, there are holes at x =0, pi, 2pi, etc, and vertical asymptotes at x = pi/2, 3pi/2, etc

    Should't the answer be y= 1 / cos^2(x) ?
    And can someone please explain to me how you find holes in this type of function?
    Thanks!
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  2. #2
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    Quote Originally Posted by ringo View Post
    this question was given on a practice test

    y = sec(x)csc(x)tan(x) Determine if there are any vertical asymptotes or holes

    The answer given was
    Y = sin(x)/[cos(x)sin(x)] = 1/cos(x)
    Therefore, there are holes at x =0, pi, 2pi, etc, and vertical asymptotes at x = pi/2, 3pi/2, etc

    Should't the answer be y= 1 / cos^2(x) ?
    And can someone please explain to me how you find holes in this type of function?
    Thanks!
    \sec{x}\csc{x}\tan{x} = \frac{\sin{x}}{\sin{x}\cos^2{x}}<br />

    "holes" wherever \sin{x} = 0

    vertical asymptotes wherever \cos{x} = 0
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  3. #3
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    Thank you, that makes more sense now.
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