Question

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

Answer 1

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

Answer 2

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

Answer 3

tan is opposite over adjacent. arctan of 2 means 2 is the sides so\[\tan x=\frac{ 2 }{ 1 }\]

Answer 4

sin is opposite over hypotenuse. lets find that.

Answer 5

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

Answer 6

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

Answer 7

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