Find the Exact Value tan(630 degrees )

Rewrite ${\displaystyle \tan \left(630°\right)}$ in terms of sines and cosines.

Remove full rotations of ${\displaystyle 360}$° until the angle is between ${\displaystyle 0}$° and ${\displaystyle 360}$°.

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the third quadrant.

The exact value of ${\displaystyle \cos \left(90\right)}$ is ${\displaystyle 0}$.

Multiply ${\displaystyle -1}$ by ${\displaystyle 0}$.