# How do you simplify arctan (tan 3pi/4)?

$- \frac{\pi}{4}$
To solve this you must first solve the inside. Now think about it... $\tan \left(\frac{3 \pi}{4}\right)$ equals what? It equals -1 on the unit circle. This is because tan uses both sine and cosine ( $\frac{\sin}{\cos}$) and in quadrant two, which $\frac{3 \pi}{4}$ sits in only cosine is negative making tangent a negative.
Now that we have simplified it into $\arctan \left(- 1\right)$ we can find what special radian that is on the unit circle. Remember that $\arctan$ is limited to quadrants one and four. So the only answer left is the value $- \frac{\pi}{4}$ in quadrant four.