`-105^@` Find the exact values of the sine, cosine, and tangent of the angle.

`-105^@=30^@-135^` 

`sin(u-v)=sin(u)cos(v)-cos(u)sin(v)`

`sin(30-135)=sin(30)cos(135)-cos(30)sin(135)`

`sin(30-135)=(1/2)(-sqrt2/2)-(sqrt3/2)(sqrt2/2)=-sqrt2/4(1+sqrt3)`

`cos(u-v)=cos(u)cos(v)+sin(u)sin(v)`

`cos(30-135)=cos(30)cos(135)+sin(30)sin(135)`

`cos(30-135)=(sqrt3/2)(-sqrt2/2)+(1/2)(sqrt2/2)=sqrt2/4(-sqrt3+1)`

`tan(u-v)=(tan(u)-tan(v))/(1+tan(u)tan(v))`

`tan(30-135)=(tan(30)-tan(135))/(1+tan(30)tan(135))`

`tan(30-135)=((sqrt3/3)-(-1))/(1+(sqrt3/3)(-1))=((sqrt3+3)/3)/((3-sqrt3)/3)=(sqrt3+3)/(3-sqrt3)`

After the denominator is rationalized the answer is `2+sqrt3.`