Question

How do you find all six trigonometric functions of 240 degrees?

Answer 1

`240^o` has a reference angle of `60^o` as indicated in the image below. A `60^o` angle is a basic angle from one of the common triangles:

From their definitions:

`sin(240^o) = -sqrt(3)/2`

`cos(240^o) = -1/2`

`tan(240^o) = sqrt(3)`

`csc(240^o) = - 2/sqrt(3)`

`sec(240^o) = -2`

`cot(240^o) = 1/sqrt(3)`

Answer 2

There is another way, using the trig unit circle.

`sin 240 = sin (60 + 180) = -sin 60 = -(sqr3)/2` (trig table)

`cos 240 = cos (60 + 180) = -cos 60 = -1/2`

`tan 240 = sin 240/cos 240 = sqr3`

`cot 240 = = 1/(sqr3) = (sqr3)/3`

`sec 240 = 1/sin 240 = - (2sqr3)/3`

`csc 240 = 1/cos 240 = -2`