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18 February, 11:06

An angle measuring (870n) ° is in standard position. For which value of n will the terminal side fall on the y-axis? n = 3 n = 4 n = 5 n = 6

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  1. 18 February, 11:44
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    The answer is n=3

    Step-by-step explanation:

    Given that an angle measuring (870n) ° is in standard position.

    we have to find the value of n for which the terminal side fall on the y-axis.

    If it can written in the form of (90°) a, where a is any positive odd integer.

    The terminal side fall on y-axis when a is positive odd integer.

    Here, the given angle is (870n) °,

    For n = 3,

    Our angle will be 2610°

    Its terminal side fall along the positive portion of the y-axis,

    If 2610° = (90°) a ⇒ a = 29 (Positive odd integer)

    Thus, for n = 3, the terminal side of the angle (870n) ° falls along the positive portion of the y-axis,

    For n = 4,

    Our angle will be 3480°

    Its terminal side fall along the positive portion of the y-axis,

    If 3480° = (90°) a ⇒ a = 38.6667 (Not possible)

    Thus, for n = 4, the terminal side of the angle (870n) ° does not fall along the positive portion of the y-axis

    For n = 5,

    Our angle will be 4350°

    Its terminal side fall along the positive portion of the y-axis,

    If 4350° = (90°) a ⇒ a = 48.333 ... (Not possible)

    Thus, for n = 5, the terminal side of the angle (870n) ° does not fall along the positive portion of the y-axis,

    For n = 6,

    Our angle will be 5220°

    Its terminal side fall along the positive portion of the y-axis,

    If 5220° = (90°) a ⇒ a = 58 (Not possible)

    Thus, for n = 6, the terminal side of the angle (870n) ° does not fall along the positive portion of the y-axis.
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