Mathematics

Mathematics

Problem

If an angle xx lies in the second quadrant, the sign of tan⁡x\tan x is a) Positive b) Negative c) Not defined d) Zero
Intuitive explanation

In the second quadrant, sine is positive but cosine is negative. Since tan⁡x=sin⁡xcos⁡x\tan x = \frac{\sin x}{\cos x}, you're dividing a positive number by a negative number, which always gives a negative result. The key is remembering which trig functions are positive in each quadrant—here, only sine and cosecant survive in quadrant II.

Intuitive explanation

In the second quadrant, sine is positive but cosine is negative. Since tan⁡x=sin⁡xcos⁡x\tan x = \frac{\sin x}{\cos x}, you're dividing a positive number by a negative number, which always gives a negative result. The key is remembering which trig functions are positive in each quadrant—here, only sine and cosecant survive in quadrant II.

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