Question

In Which Quadrant is this true

Answer 1

Given:

`\sin \theta <0`

`\tan \theta <0`

To find:

The quadrant in which
`\theta` lie.

Solution:

Quadrant concept:

In Quadrant I, all trigonometric ratios are positive.

In Quadrant II, only
`\sin\theta` and
`\csc\theta` are positive.

In Quadrant III, only
`\tan\theta` and
`\cot\theta` are positive.

In Quadrant IV, only
`\cos\theta` and
`\sec\theta` are positive.

We have,

`\sin \theta <0`

`\tan \theta <0`

Here,
`\sin\theta` is negative and
`\tan\theta` is also negative. It is possible, if
`\theta` lies in the Quadrant IV.

Therefore, the correct option is D.