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keelyjm

help with inverse trig functions?

  • one year ago
  • one year ago

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

    • one year ago
  2. AravindG
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    well first try to make than tan inverse inside the bracket to sin inverse so that we get sin (sin-1)

    • one year ago
  3. AravindG
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    drawing a triangle can help you do that

    • one year ago
  4. keelyjm
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    Drawing a triangle will help change tan-1 to sin-1?

    • one year ago
  5. hartnn
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    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 ??

    • one year ago
  6. AravindG
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    yep :) just draw ..you will see

    • one year ago
  7. hartnn
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    once you find the hypotenuse, find sin x.

    • one year ago
  8. keelyjm
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    sqrt 5

    • one year ago
  9. hartnn
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    because sin(arctan(2)). = sin x

    • one year ago
  10. hartnn
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    yes, so sin x = sin (arctan 2) =...?

    • one year ago
  11. keelyjm
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    sqrt5?

    • one year ago
  12. hartnn
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    thats the hypotenuse . sin ratio = opposite side / hypotenuse =... ?

    • one year ago
  13. keelyjm
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    oh so it's 2/sqrt5

    • one year ago
  14. hartnn
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    yup .

    • one year ago
  15. hartnn
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    any doubts ?

    • one year ago
  16. keelyjm
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    alright and what about finding the exact real value of arccos(sqrt2/2)?

    • one year ago
  17. keelyjm
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    no I understand that now that you have to use a tiangle to solve it

    • one year ago
  18. hartnn
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    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....

    • one year ago
  19. hartnn
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    also, next time please ask new question in new post...

    • one year ago
  20. keelyjm
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    okay sorry. I am not sure how you got cos x = sqrt2/2 = 1/sqrt 2 ?

    • one year ago
  21. hartnn
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    you know unit circle ? which defines standard values of sin/cos for standard angles...

    • one year ago
  22. hartnn
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    i suggest you learn and remember all standard angles and values..

    • one year ago
  23. keelyjm
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    yes i know the unit circle. is that pi/4? 45 degrees?

    • one year ago
  24. hartnn
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    yes, exactly :)

    • one year ago
  25. keelyjm
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    so pi/4 would be the exact real value?

    • one year ago
  26. satellite73
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    \[\arccos(\frac{\sqrt{2}}{2})\] see if you recall an angle whose cosine is \(\frac{\sqrt{2}}{2}\)

    • one year ago
  27. hartnn
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    yes. pi/4 in radians 45 in degrees.

    • one year ago
  28. keelyjm
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    Thank you so much!

    • one year ago
  29. hartnn
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    welcome ^_^

    • one year ago
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