Question

Find the exact value of sin(arctan(2)). For full credit, explain your reasoning.

Answer 1

draw a triangle

Answer 2

since you can think of tangent as "opposite over adjacent" if you draw an triangle with the opposite side x and the adjacent side 1, then the angle is the arctangent of x

Answer 3

oooh you wanted 2 not x, ok we can do that too

Answer 4

all you need is the hypotenuse, which you find via pyhagoras
it is
\[\sqrt{1^2+2^2}=\sqrt5\]

Answer 5

then you can find the sine, cosine whatever
in this case the sine is \(\frac{2}{\sqrt6}\) and the cosine is \(\frac{1}{\sqrt5}\)

Answer 6

so after I find the sine and cosine what do I do

Answer 7

you were done at sine

Answer 8

\[ \sin(\arctan(2))=\frac{2}{\sqrt5}\]

Answer 9

so how can I explain that ? I say that I drew the traingle and found the son and cos and hypotenues ?

Answer 10

i will let you explain it for yourself
if you understood my explanation you can either rephrase it or copy it verbatim