Chapter 4, Problem 1RE

To determine

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

Answer to Problem 1RE

  $\frac{23\pi }{4}\text{and -}\frac{\pi }{4}$

Explanation of Solution

Given:

  $\frac{15\pi }{4}$

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 startedits same loops.

  ${\text{πradian=180}}^{\text{0}}$

or

  ${\text{2πradian=360}}^{\text{0}}$

Calculation:

Let us rewrite the angle $\frac{15\pi }{4}$ as

$\frac{15\pi }{4}=4\pi -\frac{\pi }{4}$ = ${675}^o$ which lies in the 4^th quadrant.

Since the angle lies in ${\text{4}}^{\text{th}}$ quadrant as depicted by the standard position figure.

Hence, Conterminal angles for the given angles are

  $\text{2}\pi \text{+}\frac{15\pi }{4}=\frac{23\pi }{4}\text{and -}\frac{\pi }{4}$