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Question

Determine the quadrant when the terminal side of the angle lies according to the following conditions: tan(t)>0,cosec(t)<0


A

Quadrant I

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B

Quadrant III

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C

Quadrant IV

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D

Quadrant II

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Solution

The correct option is B

Quadrant III


Trigonometry functions in all quadrant:

In the first quadrant the trigonometric function sin(t),cos(t),tan(t),cosect,sect,cott all are positive.

In the second quadrant trigonometric function sin(t),cosect are positive.

In the third quadrant trigonometric function tan(t),cott are positive.

In the fourth quadrant trigonometric function cos(t),sect are positive.

In the first quadrant tan(t)>0 but cosect<0 is not possible.

Thus, first option is discarded.

Thus, cosect<0 in third and fourth quadrant and tan(t)>0 in the third quadrant.

Thus, second option is correct.

In the fourth quadrant tan(t)>0 but cosect<0 are not possible.

Thus, third option is discarded.

In the second quadrant tan(t)>0 and cosect<0 are not possible.

Hence, fourth option is discarded.

Therefore, option B is the correct answer.


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