Answer to Question #244737 in Trigonometry for Carmen

Question

If $\theta$ is an angle in the third quadrant, in which quadrant does the point (sin$\theta$ cos$\theta$ , sin$\theta$ +cos$\theta$ ) lie?

Answer 1

Given that $\theta$ is in the third quadrant.

$\therefore sin\theta$ is negative and $cos\theta$ is also negative.

So, $sin\theta.cos\theta$ is positive and $sin\theta+cos\theta$ is negative.

$\therefore x-coordinate$ is positive and $y-coordinate$ is negative.

So, (sin$\theta$ cos$\theta$ , sin$\theta$ +cos$\theta$ ) lies in fourth quadrant.