Question

Find a positive angle less than one rotation that is coterminal of -4pi/3

Answer 1

 -4pi/3 =＞ 2pi + (-4pi/3)
-4pi/3=>6pi/3 + (-4pi/3)
-4pi/3=>2pi/3
Hope it helps :)

Answer 2

Answer:

The coterminal angle is $\frac{2\pi}{3}$

Step-by-step explanation:

In order to find a positive coterminal angle, we must have to add $2\pi$ to the angle:

$2\pi + (-\frac{4\pi}{3})=2\pi -\frac{4\pi}{3}$

Applying the rule for substraction of an integer and a fraction:

$a-\frac{b}{c} = \frac{(a)(c)-b}{c}$

In this case:

$a=2\pi\\b=4\pi\\c=3$

Therefore:

$2\pi-\frac{4\pi}{3}=\frac{(2\pi)(3)-4\pi}{3}=\frac{6\pi-4\pi}{3}=\frac{2\pi}{3}$