In what quadrant is an angle whose sine is positive and tangent is negative?

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- Jun 21st 2005, 12:57 PMTiffychopWhat quadrant is this in?
In what quadrant is an angle whose sine is positive and tangent is negative?

- Jun 22nd 2005, 02:47 AMticbol
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.