Question

Evaluate arctan(tan(2pi/3))

Answer 1

For this case we know that
`(2\pi)/(3)= 120 degrees`. For this case we want to find:

`arctan(tan((2\pi)/(3)))`

Since the tan and arctan functions are inverse when we apply bth at the same time we got the identity function so then we got for this case:

`arctan(tan((2\pi)/(3))) = I((2\pi)/(3)) = (2\pi)/(3)`

Explanation:

For this case we know that
`(2\pi)/(3)= 120 degrees`. For this case we want to find:

`arctan(tan((2\pi)/(3)))`

Since the tan and arctan functions are inverse when we apply bth at the same time we got the identity function so then we got for this case:

`arctan(tan((2\pi)/(3))) = I((2\pi)/(3)) = (2\pi)/(3)`