`-(13pi)/12` Find the exact values of the sine, cosine, and tangent of the angle.

`sin((-13pi)/12)`

using the property sin(-x)=-sin(x),

`sin((-13pi)/12)=-sin((13pi)/12)`

`=-sin(pi/2+pi/3+pi/4)`

Now using sin(pi/2+x)=cos(x),

`=-cos(pi/3+pi/4)`

`=-(cos(pi/3)cos(pi/4)-sin(pi/3)sin(pi/4))`

`=-(1/2*1/sqrt(2)-sqrt(3)/2*1/sqrt(2))`

`=(sqrt(3)-1)/(2sqrt(2))`

rationalizing the denominator,

`=(sqrt(2)(sqrt(3)-1))/4`

`cos((-13pi)/12)`

using the property cos(-x)=cos(x),

`cos((-13pi)/12)=cos((13pi)/12)`

`cos((13pi)/12)=cos(pi/2+pi/3+pi/4)`

now using cos(pi/2+x)=-sin(x),

`=-sin(pi/3+pi/4)`

`=-(sin(pi/3)cos(pi/4)+cos(pi/3)sin(pi/4))`

`=-(sqrt(3)/2*1/sqrt(2)+1/2*1/sqrt(2))`

`=(-(sqrt(3)+1))/(2sqrt(2))` 

rationalizing the denominator,

`=(-sqrt(2)(sqrt(3)+1))/4`  

`tan((-13pi)/12)=sin((-13pi)/12)/cos((-13pi)/12)`

plug in the values of `sin((-13pi)/12),cos((-13pi)/12)` obtained above,

`=((sqrt(2)(sqrt(3)-1))/4)/((-sqrt(2)(sqrt(3)+1))/4)`

`=-(sqrt(3)-1)/(sqrt(3)+1)` 

rationalizing the denominator,

`=-((sqrt(3)-1)(sqrt(3)-1))/((sqrt(3)+1)(sqrt(3)-1))`

`=-(3+1-2sqrt(3))/2`

`=-(4-2sqrt(3))/2`

`=sqrt(3)-2`