Question

Find the measures of two angles, one positive and one negative, that are coterminal with
`(\pi)/(5)`.


`a. (11\pi)/(5) ; (-9\pi)/(5) \\b. (\pi)/(5) + 360^o ; (\pi)/(5) - 360^o \\c. (6\pi)/(5) ; (-4\pi)/(5) \\d. (11\pi)/(5) ; (-\pi)/(5)`

Answer 1

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

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