anonymous
  • anonymous
help with inverse trig functions?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Find the exact value of sin(arctan(2)). For full credit, explain your reasoning.
AravindG
  • AravindG
well first try to make than tan inverse inside the bracket to sin inverse so that we get sin (sin-1)
AravindG
  • AravindG
drawing a triangle can help you do that

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anonymous
  • anonymous
Drawing a triangle will help change tan-1 to sin-1?
hartnn
  • hartnn
Let arctan 2 = x so, tan x = 2 /1 since you know tan x = opposite side/adjacent side make a right angled triangle with one leg =2 and other leg = 1 |dw:1359734613467:dw| now can you find the hypotenuse ??
AravindG
  • AravindG
yep :) just draw ..you will see
hartnn
  • hartnn
once you find the hypotenuse, find sin x.
anonymous
  • anonymous
sqrt 5
hartnn
  • hartnn
because sin(arctan(2)). = sin x
hartnn
  • hartnn
yes, so sin x = sin (arctan 2) =...?
anonymous
  • anonymous
sqrt5?
hartnn
  • hartnn
thats the hypotenuse . sin ratio = opposite side / hypotenuse =... ?
anonymous
  • anonymous
oh so it's 2/sqrt5
hartnn
  • hartnn
yup .
hartnn
  • hartnn
any doubts ?
anonymous
  • anonymous
alright and what about finding the exact real value of arccos(sqrt2/2)?
anonymous
  • anonymous
no I understand that now that you have to use a tiangle to solve it
hartnn
  • hartnn
arccos(sqrt2/2) =x cos x = sqrt2/2 = 1/sqrt 2 for what value of angle 'x' is cos x = 1/sqrt 2 its one of the standard angle....
hartnn
  • hartnn
also, next time please ask new question in new post...
anonymous
  • anonymous
okay sorry. I am not sure how you got cos x = sqrt2/2 = 1/sqrt 2 ?
hartnn
  • hartnn
you know unit circle ? which defines standard values of sin/cos for standard angles...
hartnn
  • hartnn
i suggest you learn and remember all standard angles and values..
anonymous
  • anonymous
yes i know the unit circle. is that pi/4? 45 degrees?
hartnn
  • hartnn
yes, exactly :)
anonymous
  • anonymous
so pi/4 would be the exact real value?
anonymous
  • anonymous
\[\arccos(\frac{\sqrt{2}}{2})\] see if you recall an angle whose cosine is \(\frac{\sqrt{2}}{2}\)
hartnn
  • hartnn
yes. pi/4 in radians 45 in degrees.
anonymous
  • anonymous
Thank you so much!
hartnn
  • hartnn
welcome ^_^

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