How do you simplify the expression $sin (arctan (2))$ $sin(arctan(2))$ ?

Question

2067 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-11-19T16:39:06

$sin (arctan (2))$ $sin(arctan(2))$ does not exist.

$sin (arctan (2)) = θ$ $sin(arctan(2))=theta$ ,

then $sin θ = tan 2$ $sintheta=tan2$ , where angle $2$ $2$ is in radians.

As $2$ $2$ is in radians and it is less than $\frac{3 π}{4} = 2.356$ $(3pi)/4=2.356$

Hence $tan 2 < tan (\frac{3 π}{4})$ $tan2<tan((3pi)/4)$ i.e. $tan 2 < - 1$ $tan2<-1$

Therefore $sin θ < - 1$ $sintheta<-1$ ,

but this is not possible.

Hence, $sin (arctan (2))$ $sin(arctan(2))$ does not exist.

How do you simplify the expression sin(arctan(2))sin(arctan(2))sin(arctan(2))?