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

The coterminal angle is
`(2\pi)/(3)`

Explanation:

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

`2\pi + (-(4\pi)/(3))=2\pi -(4\pi)/(3)`

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

`a-(b)/(c) = ((a)(c)-b)/(c)`

In this case:

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

Therefore:

`2\pi-(4\pi)/(3)=((2\pi)(3)-4\pi)/(3)=(6\pi-4\pi)/(3)=(2\pi)/(3)`