Chapter 4, Problem 2RE

To determine

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

Answer to Problem 2RE

  $\frac{2\pi }{3}\text{ and -}\frac{10\pi }{3}$

Explanation of Solution

Given:

  $-\frac{4\pi }{3}$

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

  ${\text{2πradian=360}}^{\text{0}}$

Calculation:

Let us rewrite the angle $-\frac{4\pi }{3}$ ,as

$2\pi -\frac{4\pi }{3}$ = $\frac{2\pi }{3}$ = ${\text{120}}^0$ which lies in 2^nd quadrant.

As depicted by the standard position figure, it is clear that the angle lies in the 2^nd quadrant.

Hence, Coterminal angles for the given angles are,

  $2\pi -\frac{4\pi }{3}=\frac{2\pi }{3}\text{ and -}\frac{10\pi }{3}$