Find the exact values of the sine, cosine, and tangent of 13π/12.

sin(13π/12)=

cos(13π/12)=

tan(13π/12)=

-1/√3

Use the sum and difference formulas for sine, cosine, and tangent.

13π/12=5π/4-π/6

sin(13π/12)=sin(5π/4-π/6)=sin(5π/4)cos(π/6)-cos(5π/4)sin(π/6)

=(-√2/2)(√3/2)-(-√2/2)(1/2)=

cos(13π/12)=cos(5π/4-π/6)=cos(5π/4)cos(π/6)+sin(5π/4)sin(π/6)

=(-√2/2)(√3/2)+(-√2/2)(1/2)=

tan(13π/12)=tan(5π/4-π/6)=