State the quadrant in which θ lies.

sin(θ) < 0 and cos(θ) < 0

both are negative? What is quadrant III?

To determine the quadrant in which θ lies, we need to consider the signs of sin(θ) and cos(θ).

Given that sin(θ) < 0 and cos(θ) < 0:

1) sin(θ) < 0 means that the sine of θ is negative.

2) cos(θ) < 0 means that the cosine of θ is negative.

Based on these conditions, we can conclude that θ lies in the third quadrant.

In the third quadrant, both sine and cosine are negative.

To determine the quadrant in which θ lies, we need to look at the signs of the sine (sin) and cosine (cos) functions.

Given that sin(θ) < 0 and cos(θ) < 0, it means that both the sine and cosine values are negative.

In the Cartesian coordinate system, the signs of the sine and cosine functions can be associated with the four quadrants as follows:

- In the first quadrant (Q1), both sin(θ) and cos(θ) are positive.
- In the second quadrant (Q2), sin(θ) is positive but cos(θ) is negative.
- In the third quadrant (Q3), both sin(θ) and cos(θ) are negative.
- In the fourth quadrant (Q4), sin(θ) is negative but cos(θ) is positive.

Since sin(θ) < 0 and cos(θ) < 0, it indicates that θ is in the third quadrant (Q3).