`(5pi)/12` Find the exact values of the sine, cosine, and tangent of the angle.

`(5pi)/12=pi/4+pi/6`

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

`sin(pi/4+pi/6)=sin(pi/4)cos(pi/6)+cos(pi/4)sin(pi/6)`

`sin(pi/4+pi/6)=(sqrt2/2)(sqrt3/2)+(sqrt2/2)(1/2)=sqrt2/4(sqrt3+1)`

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

`cos(pi/4+pi/6)=cos(pi/4)cos(pi/6)-sin(pi/4)sin(pi/6)`

`cos(pi/4+pi/6)=(sqrt2/2)(sqrt3/2)-(sqrt2/2)(1/2)=sqrt2/4(sqrt3-1)`

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

`tan(pi/4+pi/6)=(tan(pi/4)+tan(pi/6))/(1-tan(pi/4)tan(pi/6))=(1+(sqrt3/3))/(1-(1)(sqrt3/3))=((3+sqrt3)/3)/((3-sqrt3)/3)=(3+sqrt3)/(3-sqrt3)`

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