# How do you find the quadrants in which the terminal side of theta must lie given sintheta is positive and cos theta is negative?

Jul 12, 2017

$\theta$ is in $Q 2$.

#### Explanation:

$\sin \theta$ is postive in $Q 1$ and $Q 2$, it is negative in $Q 3$ and $Q 4$ - so is $\csc \theta$ as it is its reciprocal.

$\cos \theta$ is positive in $Q 1$ and $Q 4$, it is negative in $Q 2$ and $Q 3$ - so is its reciprocal $\sec \theta$.

$\tan \theta$ is positive in $Q 1$ and $Q 3$ and it is negative in $Q 2$ and $Q 4$ - so is $\cot \theta$ as it is its reciprocal.

As $\sin \theta$ is positive and $\cos \theta$ is negative,

$\theta$ is in $Q 2$.