Question

Find the measures of two angles, one positive and one negative, that are coterminal with ac%7B%5Cpi%7D%7B5%7D" id="TexFormula1" title="\frac{\pi}{5}" alt="\frac{\pi}{5}" align="absmiddle" class="latex-formula">.
$a. \frac{11\pi}{5} ; \frac{-9\pi}{5} \\b. \frac{\pi}{5} + 360^o ; \frac{\pi}{5} - 360^o \\c. \frac{6\pi}{5} ; \frac{-4\pi}{5} \\d. \frac{11\pi}{5} ; \frac{-\pi}{5}$

Answer 1

Answer:

a. 11/5 pi; -9/5 pi

Step-by-step explanation:

Coterminal angles are those which have a common terminal side. For example 30° is coterminal with −330° and 390° (see figure).

From the example we can see that the following expressions must be fulfilled:

positive angle - reference angle = 360°

reference angle - negative angle = 360°

where positive angle is 390°, reference angle is 30° and negative angle is -330°. In this problem reference angle is pi/5. Also, we have to change 360° for its equivalent in radians, i. e., 2 pi. So,

positive angle - pi/5 = 2 pi

positive angle = 2 pi + pi/5

positive angle = 11/5 pi

pi/5 - negative angle = 2 pi

negative angle = pi/5 - 2 pi

negative angle = -9/5 pi