How do you simplify $arctan (sin (\frac{7 π}{2}))$ $arctan(sin((7pi)/2))$ ?

Question

1792 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-05-02T13:13:36

$arctan (sin (7 \frac{π}{2})) = - \frac{π}{4}$ $arctan(sin(7pi/2))=-pi/4$

As $sin (\frac{7 π}{2}) = sin (4 π - \frac{π}{2}) = - sin (\frac{π}{2}) = - 1$ $sin((7pi)/2)=sin(4pi-pi/2)=-sin(pi/2)=-1$

$arctan (sin (7 \frac{π}{2})) = arctan (- 1)$ $arctan(sin(7pi/2))=arctan(-1)$

As $tan (- \frac{π}{4}) = - 1$ $tan(-pi/4)=-1$

$arctan (- 1) = - \frac{π}{4}$ $arctan(-1)=-pi/4$

Hence $arctan (sin (7 \frac{π}{2})) = - \frac{π}{4}$ $arctan(sin(7pi/2))=-pi/4$

How do you simplify arctan(sin((7pi)/2))arctan(sin(7π2)) arctan(sin((7pi)/2))?