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What is the range of the function y = |2cscθ| - 1?

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  • 6 months ago
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    We know:

    csc θ = 1 / sin θ

    Since -1 ≤ sin θ ≤ 1, the reciprocal will be:

    csc θ ≤ -1 or csc θ ≥ 1

    If you double it:

    2 csc θ ≤ -2 or 2 csc θ ≥ 2

    When you take the absolute value, you get:

    |2 csc θ| ≥ 2

    And then when you subtract 1, you get:

    |2 csc θ| - 1 ≥ 1

    Answer:

    [1, ∞)

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