Find the exact value of sin(arctan(2)). For full credit, explain your reasoning. I really need this for precalcc!

Question

anonymous · Answer

$$\sin(\tan^{-1}(2))$$$$\sin(\frac{ \cos(2) }{ \sin(2) })$$hmm... What next?! What do you think?

anonymous · Answer

should we draw a triangle... Let's see

anonymous · Answer

tan is opposite over adjacent. arctan of 2 means 2 is the sides so$$\tan x=\frac{ 2 }{ 1 }$$|dw:1355376223111:dw|

anonymous · Answer

sin is opposite over hypotenuse. lets find that.

anonymous · Answer

1^2 + 2^2 = c^2
1 + 4 = c^2
$$\sqrt5 = c$$Which is the hypotenuse

anonymous · Answer

$$\sin x = \frac{ 2 }{ \sqrt5 }$$$$\frac{ 2 }{ \sqrt 5 }$$thats the answer. is it okay to leave it in this form of a fraction?

anonymous · Answer

To explain you should draw the triangle, solve for the hypotenuse, and say that arctan is x, so you just have to find the sin of x. And we are not solving for x, we are solving for what sin(x) is. remember that we already kno x, which is arctan2