Question

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

Answer 1

`-(pi)/4`

Explanation:

To solve this you must first solve the inside. Now think about it... `tan((3pi)/4)` equals what? It equals -1 on the unit circle. This is because tan uses both sine and cosine ( `sin/cos`) and in quadrant two, which `(3pi)/4` sits in only cosine is negative making tangent a negative.

Now that we have simplified it into `arctan(-1)` 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 `-(pi)/4` in quadrant four.

Here is the work written out if this helps you more.