# Math Help - Which quadrant is this in?

1. ## What quadrant is this in?

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

2. Maybe you are studying these:
>>>reference triangle
>>>opposite side = y
>>>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.