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

well first try to make than tan inverse inside the bracket to sin inverse so that we get sin (sin-1)

drawing a triangle can help you do that

Drawing a triangle will help change tan-1 to sin-1?

yep :) just draw ..you will see

once you find the hypotenuse, find sin x.

sqrt 5

because sin(arctan(2)). = sin x

yes, so sin x = sin (arctan 2) =...?

sqrt5?

thats the hypotenuse .
sin ratio = opposite side / hypotenuse =... ?

oh so it's 2/sqrt5

yup .

any doubts ?

alright and what about finding the exact real value of arccos(sqrt2/2)?

no I understand that now that you have to use a tiangle to solve it

also, next time please ask new question in new post...

okay sorry. I am not sure how you got cos x = sqrt2/2 = 1/sqrt 2 ?

you know unit circle ?
which defines standard values of sin/cos for standard angles...

i suggest you learn and remember all standard angles and values..

yes i know the unit circle. is that pi/4? 45 degrees?

yes, exactly :)

so pi/4 would be the exact real value?

\[\arccos(\frac{\sqrt{2}}{2})\] see if you recall an angle whose cosine is \(\frac{\sqrt{2}}{2}\)

yes.
pi/4 in radians
45 in degrees.

Thank you so much!

welcome ^_^