Question

Find the exact value of sin(arctan(2)).

Answer 1

Do you have guess?
Hint: arctan(2) is same as tan(y)=2

Answer 2

I'm just unsure of how to solve it on paper, but yeah i know that tan(y) = 2

Answer 3

well, use it to draw a triangle and label the appropriate sides.

Answer 4

what should be opposite and adjacent respectively given you know\[\tan(y)=2\]

Answer 5

so its tan(y) = 2/1?

Answer 6

Perfect!

Answer 7

and then where does it go from there? the answer isnt one

Answer 8

Now what is sin(y) using same triangle?

Answer 9

sin is opposite over hypotenuse

Answer 10

oh i got it! its radical 5

Answer 11

but you don't have hypotenuse, how will you calculate it?

Answer 12

so now all i do is 2/ radical 5?

Answer 13

yes, that's correct!