Question

From the information given determine the quadrant in which the terminal point (determined by an angle with a measure of a) lies. Input I, II, III, or IV.

If sin(θ)<0 and cos(θ)<0), then (x,y) lies in quadrant ___

If sin(θ)>0 and cos(θ)<0), then (x,y) lies in quadrant ____

If sin(θ)>0 and cos(θ)>0), then (x,y) lies in quadrant ____

If sin(θ)<0 and cos(θ)>0), then (x,y) lies in quadrant ____
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Answer 1

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.

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.