`(2pi)/3` Evaluate the sine, cosine and tangent of the angle without using a calculator.

Textbook Question

Chapter 4, 4.4 - Problem 59 - Precalculus (3rd Edition, Ron Larson).
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kspcr111 | In Training Educator

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1)

`sin(2pi/3) = sin(pi- pi/3) `

As we know that `sin(pi-x) = sin(x)`

so ,

`sin(pi- pi/3) = sin(pi/3) = sqrt(3)/2`

2)

`cos(2pi/3) = cos (pi- pi/3)`

As we know that `cos(pi-x) = -cos(x)`

so,

`cos(pi- pi/3) = -cos(pi/3) = -1/(2)`

3)

`Tan(2pi/3)= (sin(2pi/3))/(cos(2pi/3)) = (sqrt(3)/2)/(-1/(2))= -sqrt(3)`

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