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

2 Answers
May 8, 2015

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:
enter image source here

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)

May 10, 2015

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