Chapter 12.1, Problem 17OE

To determine

To determine the quadrant of given angle.

Answer to Problem 17OE

The given angle is in IV quadrant.

Explanation of Solution

Given information :

  $-{400}^{\circ }$

The given angle is more than ${360}^{\circ }$ . This means the angle has covered whole circle and then again started from the starting point.

In such cases when angles are more than ${360}^{\circ }$ , to determine quadrant we subtract ${360}^{\circ }$ from the given angle, till it becomes less than ${360}^{\circ }$ .

Here the negative sign denotes that the angle is clockwise. This angle covered whole circle clockwise with $-{360}^{\circ }$ and then remaining $-{40}^{\circ }$ from the starting point.

Now we shall convert it in anticlockwise direction by subtracting the angle from ${360}^{\circ }$

Hence we get,

  ${360}^{\circ }-{40}^{\circ }={320}^{\circ }$

Angles between ${270}^{\circ }$ and ${360}^{\circ }$ lies in IV quadrant.

Hence the angle lies in IV quadrant.