Question

If sinθ <0 and tanθ <0 then:

A. 180°<θ<270°

B. 270°<θ<360°

C. 0°<θ<90°

D. 90°<θ<180°​

Answer 1

sin(θ) < 0 is another way of saying the sin(θ) is negative, and that happens on Quadrants III and IV.

tan(θ) < 0 is another way of saying the tan(θ) is negative, and since tangent = sine/cosine, that can only happen when the sine and cosine are both of different signs, and that only occurs on Quadrants II and IV.

when is the sine negative as well as the tangent? when the sine is negative and the cosine is positive, and that'd be on Quadrant IV, 270° < θ < 360°.

Answer 2

B

Explanation:

sinΘ < 0 in third and fourth quadrant

tanΘ < 0 in second and fourth quadrants

So both trig ratios are < 0 in the fourth quadrant (270 - 360 )

Hence 270° < Θ < 360° → B