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

Question

16996 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-12-28T18:26:57

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

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

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

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

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

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

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

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