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