Question

How do you evaluate sine, cosine, tangent of `(10pi)/3` without using a calculator?

Answer 1

`sin((10pi)/3)= -sqrt(3)/2`

`cos((10pi)/3)= -1/2`

`tan((10pi)/3)= sqrt(3)`

Explanation:

You consider that: `(10pi)/3 = 2pi+pi+pi/3`, so that:

`sin((10pi)/3)= sin(2pi+pi+pi/3) =sin(pi+pi/3) = sinpicos(pi/3)+cospisin(pi/3) = -sin(pi/3)= -sqrt(3)/2`

`cos((10pi)/3)= cos(2pi+pi+pi/3) =cos(pi+pi/3) = cospicos(pi/3)-sinpisin(pi/3) = -cos(pi/3)= -1/2`

`tan((10pi)/3)= sin((10pi)/3)/(cos((10pi)/3))=(-sqrt(3)/2)/(-1/2) = sqrt(3)`