Which statement is correct for the math statement? the statement:  "Tanθ=-12/5, cscθ=-13/2, and the terminal point determined by θ is in quadrant 3" which is correct? A. cannot be true because...

Which statement is correct for the math statement?

the statement:  "Tanθ=-12/5, cscθ=-13/2, and the terminal point determined by θ is in quadrant 3"

which is correct?

A. cannot be true because 12^2+5^2 ≠1

B. cannot be true because if tanθ=-12/5, then cosθ=±13/25

C. cannot be true because tanθ must be less than 1

D. cannot be true because tanθ is greater than 0 in quadrant 3

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lfryerda eNotes educator | Certified Educator

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Since the `tan theta` is negative, then the terminal arm must be in the second or fourth quadrant.  Also, since `csc theta` is negative, then the terminal arm must be in the third or fourth quadrant.  This means that the terminal arm must be in the fourth quadrant.  

However, the statement is that the terminal arm determined by theta is in quadrant 3, which is must be incorrect.  

Therefore, the answer is D, which is that `tan theta` is greater than 0 in quadrant 3, despite being told in the statement that it is negative.

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