Question

An angle whose measure is -405° is in

standard position. In what quadrant

does the terminal side of the angle fall?

Quadrant 1

Quadrant II

Quadrant III

Quadrant IV

Answer 1

Quadrant IV

Explanation:

Given

`\theta = -405^\circ`

Required

The quadrant of the terminal side

To do this, we simply rotate the given angle in a clockwise direction.

A complete rotation is
`-360^\circ`

So, we have:

`\theta = -405^\circ`

`\theta = -360^\circ -45^\circ`

Remove the complete rotation

`\theta = -45^\circ`

When
`45^\circ` is rotated in the clockwise direction, it stops at the 4th quadrant.

Hence, the terminal side falls in the quadrant IV