Angle 0 lies in the third quadrant when sin0<0 and cos 0<0. The quadrant where both sine and cosine are negative is the third quadrant.
In the Cartesian coordinate system, the quadrant in which both the sine and cosine values are negative is the third quadrant. This can be determined by understanding that the sine function represents the y-coordinate (vertical component) of a point on the unit circle and the cosine function represents the x-coordinate (horizontal component). Since the sine and cosine values are both negative, it indicates that both the x and y coordinates of the point are negative, which only occurs in the third quadrant.
The given question is asking for the quadrant in which angle 0 lies when sin0<0 and cos 0<0.
We know that sin0 represents the y-coordinate and cos 0 represents the x-coordinate of a point on the unit circle corresponding to angle 0.
When sin0<0 and cos 0<0, it means that the y-coordinate is negative and the x-coordinate is also negative. This corresponds to the third quadrant of the unit circle.