How do you simplify $arctan(sin((7pi)/2))$ ?

Question

1782 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-05-02T13:13:36

$arctan(sin(7pi/2))=-pi/4$

As $sin((7pi)/2)=sin(4pi-pi/2)=-sin(pi/2)=-1$

$arctan(sin(7pi/2))=arctan(-1)$

As $tan(-pi/4)=-1$

$arctan(-1)=-pi/4$

Hence $arctan(sin(7pi/2))=-pi/4$

How do you simplify arctan(sin((7pi)/2)) arctan(sin((7pi)/2))?