Question

Determine the quadrant where θ lies given that sinθ < 0 and tanθ > 0.

I
II
III
IV

Answer 1

The answer to this question is quadrant III. Since
sinθ = y/r and tanθ = y/x, we have, in quadrant III, x, y negative.

sinθ < 0 (r always positive) but tanθ > 0 (negative divided by negative is positive).

Answer 2

Option c. is correct.

Explanation:

if
`sin\theta` < 0 means values of
`sin\theta` will be negative.

For
`tan\theta =(sin\theta )/(cos\theta )` > 0 means positive value of
`tan\theta`

values of
`sin\theta` and
`cos\theta` both should be either > 0 or < 0 for the poitive values of
`tan\theta`. If any one, sine or cosine is negative then
`tan\theta` will be < 0

We know that for the condition
`tan\theta > 0` and
`sin\theta` < 0 value of
`cos\theta` should be negative.

Therefore,
`\theta` should lie in 3rd quadrant where
`sin\theta` and
`cos\theta` both are negative.

Option C. 3rd option is correct.