Chapter 4, Problem 3RE

To determine

Tofind:the one positive and one negative coterminal angle and quadrant where the angle lies.

Answer to Problem 3RE

The Coterminal angles for the given angles are, ${250}^0$ and $-{470}^0$ .

Explanation of Solution

Given:

  $-{110}^0$

Concept used:

There is four quadrant and it rotate from anticlockwise one quadrant has maximum angle of ${90}^0$

And once angle is ${360}^0$ it again started its same loops.

  ${\text{πradian=180}}^{\text{0}}$

or

  ${\text{2πradian=360}}^{\text{0}}$

As the angle is negative, hence it will be represented clockwise.

Calculation:

Let us consider the following angle $-{110}^0$ ,

It can also be written as

  ${360}^0-{110}^0={250}^0$ so, its lies in 3^rd quadrant.

As the angle is negative, hence it will be represented clockwise.

As depicted by the standard position figure. It is clear the angles lie in the ${\text{3}}^{\text{rd}}$ quadrant.

  ${360}^0-{110}^0={250}^0$

And ${\text{-360}}^0-{110}^0=-{470}^0$ .

Hence, The Coterminal angles for the given angles are, ${250}^0$ and $-{470}^0$ .