Need help with simple Trig!

Question

Provide an exact evaluation of the expression: tan (-285°).

Answer 1

Rewrite using sum or difference angle of tangent.  Use angle that are on the unit circle.

 

tan(330 - 45)

 

 

But since the angle is negative,

 

tan(45 - 330)

 

 

Now use the subtraction angle identity for tangent.

 

tan(45 - 330) = (tan45 - tan330) / [1 + tan45tan330)]

                    = (1 - (-(1/2)/√(3)/2)) / [1 + (-1(1/2)/√(3)/2)]

                    = [1 + (1/√3)] / [1 - (1/√3)]

 

 

Now just simplify.  Be sure to rationalize the denominator.