Question

Anybody know the right answer?

Answer 1

Quadrant I : cot(x) > 0 → -cot(x) < 0

Quadrant II : cot(x) < 0 → -cot(x) > 0

Quadrant III : cot(x) > 0 → -cot(x) < 0

Quadrant IV : cot(x) < 0 → -cot(x) > 0

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`a)\ \left((11\pi)/(6),\ -\sqrt3\right)\\\\(11\pi)/(6)\in\text{Quadrant IV, then -cot(x)} > 0,\ \text{we have}\ -\cot(11\pi)/(6)=-\sqrt3 < 0`

Answer: a)

`b)\\(2\pi)/(3)\in\text{Quadrant II},\ -\cot(x) > 0,\ \text{we have}\ (\sqrt3)/(3) > 0\\\\c)\\(5\pi)/(4)\in\text{Quadrant III},\ -\cot(x) < 0,\ \text{we have}\ -1 < 0\\\\d)\\(4\pi)/(3)\in\text{Quadrant III},\ -\cot(x) < 0,\ \text{we have}\ -(\sqrt3)/(3) < 0`

We know that one answer is only true, so we did not check the correctness of the cotangent value, only to the number sign