Question

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

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

Answer:

Option c. is correct.

Step-by-step explanation:

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

For $tan\theta =\frac{sin\theta }{cos\theta }$ > 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.