Question

What are the sine, cosine, and tangent of 2pi/3 radians?

Answer 1

2pi/3 has the same Sin, Cos, & Tan as pi/3 in QI except for the SIGNS.
2pi/3 is in QII so Cos is negative and Tangent is negative, Sine is still positive.
Sin 2pi/3 = √(3) / 2
Cos 2pi/3 = -1/2
Tan 2pi/3 = -√3

Answer 2

Sin (
`(2\ pi)/(3)`) =
`(√(3))/(2)` ,Tan (
`(2\ pi)/(3)`) = -
`√(3)`

Cos(
`(2\ \pi)/(3)`) =
`(1)/(2)`.

Explanation:

Given : 2pi/3 radians.

To find : What are the sine, cosine, and tangent .

Solution : We have given that
`(2\ pi)/(3)`.

Sin (
`(2\ pi)/(3)`)

Sin (
`(2\ pi)/(3)`) =
`(√(3))/(2)`

Tan (
`(2\ pi)/(3)`) = -
`√(3)`

Cos(
`(2\ pi)/(3)`) =
`(1)/(2)`.

Therefore, Sin (
`(2\ pi)/(3)`) =
`(√(3))/(2)`

Tan (
`(2\ pi)/(3)`) = -
`√(3)`

Cos(
`(2\ pi)/(3)`) =
`(1)/(2)`.