Question

In which quadrant does 0 lie given that sin 0<0 and cos 0<0

Answer 1

Answer:

$\theta$ must be in the third quadrant so that $\sin \theta < 0$ and $\cos \theta < 0$.

Step-by-step explanation:

We have to determine that in which quadrant the angle $\theta$ lies if $\sin \theta < 0$ and $\cos \theta < 0$.

The horizontal axis i.e. x-axis and the vertical axis i.e. y-axis divides the coordinate plane into four zones, the zone with x and y both positive is the first quadrant and rotating about the origin in anticlockwise we will find 2nd, 3rd and 4th quadrant one by one.

In the first quadrant all the trigonometrical functions $\sin \theta$, $\cos \theta$ and $\tan \theta$ are positive.

In the second quadrant only  $\sin \theta$ is positive.

In the third quadrant only $\tan \theta$ is positive i.e. $\sin \theta$ and $\cos \theta$ are negative.

In the fourth quadrant only $\cos \theta$ is positive.

Therefore, $\theta$ must be in the third quadrant so that $\sin \theta < 0$ and $\cos \theta < 0$. (Answer)