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keelyjm

  • one year ago

help with inverse trig functions?

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

  2. AravindG
    • one year ago
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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)

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

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

  5. hartnn
    • one year ago
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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 ??

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

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

  8. keelyjm
    • one year ago
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    sqrt 5

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

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

  11. keelyjm
    • one year ago
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    sqrt5?

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

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

  14. hartnn
    • one year ago
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    yup .

  15. hartnn
    • one year ago
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    any doubts ?

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

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

  18. hartnn
    • one year ago
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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....

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

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

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

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

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

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

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

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

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

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

  29. hartnn
    • one year ago
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    welcome ^_^

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