`-165^@` Find the exact values of the sine, cosine, and tangent of the angle.

`-165^@=-(120^@+45^@)` 

`sin(-165)=-sin(165)`

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

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

`[sin(-(120+45))]=-[sin(120)cos(45)+cos(120)sin(45)]`

`[sin(-(120+45))]=-[(sqrt3/2)(sqrt2/2)+(-1/2)(sqrt2/2)]=-sqrt2/4(sqrt3+1)`

`cos(-165)=cos(165)`

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

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

`cos(-(120+45))=cos(120)cos(45)-sin(120)sin(45)`

`cos(-(120+45))=(-1/2)(sqrt2/2)-(sqrt3/2)(sqrt2/2)=-sqrt2/4(1+sqrt3)`

`tan(-165)=-tan(165)`

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

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

`-tan(120+45)=-[(tan(120)+tan(45))/(1-tan(120)tan(45))]=-[(-sqrt3+1)/(1-(-sqrt3)(1))]=(sqrt3-1)/(1+sqrt3)`

After rationalizing the denominator the answer is `2-sqrt3.`