First , realize 10/3 pi is the same as 4/3 pi
4/3 pi is in the 3rd quadrant so the sine AND cosine will be negative....the tangent and cotangent will be positive
4/3 pi radians is equivalent to 240 degrees
sine is -sqrt(3)/2 or -.866 Cosine is - 1/2 tangent is sin/cos.... I think you can do that math.
Good luck with your studies!