Question

wt

Answer 1

it is easiest to do it with a picture of a triangle

Answer 2

that is a picture of a triangle with angle \(x\) and with \(\tan(x)=2\)
so \(x=\arctan(2)\) and you are looking for
\(\sin(\arctan(2))=\sin(\arctan(x))\)
to find it you need the hypotenuse of the triangle. by pythagoras it is
\[\sqrt{2^2+1^2}=\sqrt{5}\]

Answer 3

sorry i meant you are looking for \(\sin(x)\)

Answer 4

now we have completed the triangle

Answer 5

and \(\sin(x)=\sin(\arctan(2))=\frac{2}{\sqrt{5}}\)

Answer 6

yw, sorry about the typo