Answer:
If sin(θ)<0 and cos(θ)<0), then (x,y) lies in quadrant III.
If sin(θ)>0 and cos(θ)<0), then (x,y) lies in quadrant II.
If sin(θ)>0 and cos(θ)>0), then (x,y) lies in quadrant I.
If sin(θ)<0 and cos(θ)>0), then (x,y) lies in quadrant IV.
Step-by-step explanation:
Sine and cosine values, relation with quadrant:
Quadrant 1: Sine > 0, cosine > 0.
Quadrant 2: Sine > 0, cosine < 0.
Quadrant 3: Sine < 0, cosine < 0.
Quadrant 4: Sine < 0, cosine > 0.
If sin(θ)<0 and cos(θ)<0), then (x,y) lies in quadrant
Both negative, so III.
If sin(θ)>0 and cos(θ)<0), then (x,y) lies in quadrant
Sine positive, cosine negative, so II.
If sin(θ)>0 and cos(θ)>0), then (x,y) lies in quadrant
Both positive, so I.
If sin(θ)<0 and cos(θ)>0), then (x,y) lies in quadrant
Sine negative, cosine positive, so IV.
