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csc(theta) >0, tan (theta) <0 what quadrant does theta lie?

csc(theta) >0, tan (theta) <0 what quadrant does theta lie?

Math   Precalculus   
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Answer #1

Since tan(theta) is negative that means it cannot be in the third and the first quadrant.

Since, tan(theta) = height/base = y/x, in first quadtrant y and x are both positive hence tan(theta) is positive, and in the third quadrant both x and y are negative hence tan(theta) is positive.

cosec(theta) =

Since, cosec(theta) is positive in the first and the second quadtrant as both x and y are postive, in the second quadrant is positive and y is positive hence cosec(theta) is positive.

Therefore theta is in the second quadrant since both tan(theta) is negative in the second quadrant and the cosec(theta) is positive in the second quadrant.

Theta is in the second quadrant.

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