Question

How do you find the 6 trigonometric functions for 5pi/3?

Answer 1

`5pi/3` = 300 = 360 - 60 = 2`pi` - `pi/3`
sin ( 2`pi` - `pi/3` ) = - sin `pi/3` = `sqrt`3 / 2
Similarly Cos ( 2`pi` - `pi/3` ) = cos`pi/3` = 1/2.
tan ( 2`pi` - `pi/3` ) = - tan`pi/3` = - `sqrt3`

Explanation:

Taking reciprocals we can compute Cosec `5pi/3` = - 2 / `sqrt` 3'
sec `5pi/3` = 2, cot `5pi/3` = - 1 / `sqrt` 3.