`225^@ = 300^@ - 45^@` Find the exact values of the sine, cosine, and tangent of the angle.

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

`sin(300-45)=sin(300)cos(45)-cos(300)sin(45)`

`sin(300-45)=(-sqrt3/2)(sqrt2/2)-(1/2)(sqrt2/2)=-sqrt2/4(sqrt3+1)`

 

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

`cos(300-45)=cos(300)cos(45)+sin(300)sin(45)`

`cos(300-45)=(1/2)(sqrt2/2)+(-sqrt3/2)(sqrt2/2)=sqrt2/4(1-sqrt3)`

 

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

`tan(300-45)=(tan(300)-tan(45))/(1-tan(300)tan(45))=(-sqrt3-1)/(1-sqrt3(1))=(-sqrt3-1)/(1-sqrt3)`

The rationalized answer is `sqrt3+2.`

 

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