Question

I'd greatly appreciate if someone could explain this problem:

If sinΘ < 0 and tanΘ > 0 then:

A. 270° < Θ < 360°
B. 90° < Θ < 180°
C. 0° < Θ < 90°
D. 180° < Θ < 270°

I know the answer is D, but can someone please why?

Answer 1

The function sine, cosine and tangent have signs accord to the quadrant.

In the first quadratn all the trigonometric functions are positive.

In the second quadrant sine is negative,  cosine is positive and tangent is negative

In the third quadrant, sine is negative, cosine is negative and tangent is positive. This is the case indicated by sinΘ < 0 and tanΘ > 0

What are the angles In the third quadrant? 180° < Θ < 270°.

That is the justification.

Answer 2

the answer is d. 180°<Ф<270°