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

1 Answer

#-(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.
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