Find the exact values of the sine cosine and tangent of the

Find the exact values of the sine, cosine, and tangent of the angle. 11 pi/12 = pi/4 + 2 pi/3

11pi/4 = pi/4 + 2pi/3

sin(11pi/4) = sin(pi/4 + 2pi/3)

= sinpi/4cos2pi/3 +sin2pi/3cospi/4

=(1/sqrt2)(-1/2) +(sqrt3/2)(1/sqrt2)

=(sqrt3 - 1)/2sqrt2

cos(11pi/12) = cos(pi/4 +2pi/3)

= cospi/4*cos2pi/3 -sinpi/4*sin2pi/3

= (1/sqrt2)*(-1/2) - (1/sqrt2)*(sqrt3/2)

=-(1 +sqrt3)/2sqrt2)

tan(11pi/12) =sin(11pi/12) /cos(11pi/12) = -(sqrt3 -1)/(1 +sqrt3)