Verified answer

Keep this in mind

Add Sugar To Coffee

I st Quadrant Add sin cos tan + ve

2nd Quadrant Sugar only Sin +ve | cos , tan - ve

3rd Quadrant To only Tangent +ve | sin , cos -ve

4th quadrant Coffee only Cos +ve | sin , tan -ve

sin +ve and cos -ve second Quadrant

Sridhar has the right idea, but even I'm having a little trouble following his work.

I use a different memory technique.

ACTS, where each letter represents a quadrant, and I label them clockwise.

A: all trig. functions are positive in the first quadrant.(Q I)

C: cosine is the only trig. function positive in the 2nd quadrant.(Q IV)

T: tangent is the only trig. function positive in the 2rd quadrant.(Q III)

S: sine is the only trig. function positive in the 2rd quadrant.(Q II)

It makes more sense if you draw an xy plane, and label each quadrant with the letter and/or trig. function.

On to the problem,

sin θ >0, so θ must be in quadrant I or II.

positive * cos θ < 0 so cosθ must be negative.

The only quadrant where sin is positive and cos is negative is the 2nd quadrant, QII.

{cosθ=x, sinθ=y}; this means that sinθ >0 only when θ is in the first and second quadrants and cosθ>0 only when θ is in the first and fourth quadrants. So θ must be in the second quadrant in order for sinθ>0 and sinθcosθ<0 (which makes cosθ negative and thus the product of sinθ and cosθ negative)

a million) sin ? > 0 in quadrants 2 and 3 sec ? < 0 in quadrants a million and a pair of undemanding quadrant is two. So ? lies in quadrant 2. 2) cot ? < 0 in quadrants 2 and four sin ?< 0 in quadrants 3 and four undemanding quadrant is 4. So ? lies in quadrant 4.

it has to b in the second quadrant bcoz in that quadrant, sine is positive and the other functionsare negative. in order for a negative value to occur, u hav to multiply a negative with a positive. sine theta will b positive, cos theta will b negative in second quadrant