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    Question

    What is the value of tan 570°

    ?
    A –1/√3 Correct Answer Incorrect Answer
    B –√3 Correct Answer Incorrect Answer
    C 1/√3 Correct Answer Incorrect Answer
    D √3 Correct Answer Incorrect Answer

    Solution

    To find tan 570Âș , we reduce the angle by subtracting multiples of 360Âș until we get an equivalent angle between 0Âș and 360Âș. 570Âș - 360Âș = 210Âș Therefore, tan(570Âș) = tan(210Âș) Now, tan(210Âș) = tan(180Âș + 30Âș) Using the formula tan(180Âș + Ξ) = tan(Ξ) , we get: tan(210Âș) = tan(30Âș) And we know: tan(30Âș) = 1/√3 However, since 210Âș is in the third quadrant where tan is positive, we have: tan(210Âș) = tan(30Âș) = 1 / √ 3 Therefore, the value of tan(570Âș) is 1 / √ 3  .

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