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Math Help - Which quadrant is this in?

  1. #1
    Newbie
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    What quadrant is this in?

    In what quadrant is an angle whose sine is positive and tangent is negative?
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  2. #2
    MHF Contributor
    Joined
    Apr 2005
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    Maybe you are studying these:
    >>>reference triangle
    >>>opposite side = y
    >>>adjacent side = x
    >>>hypotenuse = r

    So,
    We look for an angle whose sine is positive.
    sine = opp / hyp = y/r
    Since r is always positive, we need y to be positive also. Positive/positive = positive.
    y is positive above the x-axis, so y is positive in the 1st and 2nd quadrants.

    And, the angle should have a negative tangent.
    tan = opp / adj = y/x
    Since y is positive (see above), then x must be negative. Positive/negative = negative.
    x is negative to the left of the y-axis, so y is negative in the 2nd and 3rd quadrants.

    We see that the 2nd quadrant satisfies both conditions.
    Therefore, the angle is in the 2nd quadrant. ----answer.
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