A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

what is the principal value of cos^-1{cos 23pi/20}

  • This Question is Closed
  1. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\frac{17\pi}{20}\]

  2. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i think, let me check with a calculator

  3. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yeh its correct

  4. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    its an interesting method to solve , Ill do a quick picture now on paint and hopefully try to explain

  5. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok..m waitin

  6. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Well, not the best picture , but good enough . Now, first thing to notice is that the answer is not 23pi / 20 , because 23pi/20 is not in the range of cos^-1

    1 Attachment
  7. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    we must get the angle into the interval 0<x<pi

  8. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    and 23pi/20 is a bit more than pi

  9. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    hey can you tell me what is meant by principal value?? i dont know if i get the idea u knw

  10. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    however, the cos graph is symmetrical about the minimum points , that is cos(23pi /20) does equal the same value as cos (17pi /20) because they are both the same distance from the minimums

  11. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    principal value just means , "your answer must be in the range 0<x<pi" pretty much only then does cos^-1(cos(x)) = x

  12. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    if you really want to check your understanding then try \[\sin^{-1} (\sin(\frac{23\pi}{20}))\]

  13. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    its a very similar idea

  14. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    using translations of the graph , you get the angle into the range -pi/2 to pi/2 ( because the range of sin^-1 is -pi/2 to pi/2 )

  15. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    then apply sin^-1(sin(x)) = x

  16. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    hmm.. i understand what you are saying. i would like to know how you got the value 17pi/20? i know its at a distance pi/4 from 23pi/4. i wanna know if there is some other way to work it out.

  17. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    there is other ways of working it our but I dont remember them at this point in time

  18. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    hey is the prin. value for \sin^{-1} (\sin(\frac{23\pi}{20})) 13 pi/20?

  19. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\sin^{-1} (\sin(\frac{23\pi}{20})) \]

  20. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    no

  21. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    draw a picture of a sin graph this time

  22. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yea i did..

  23. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    my picture is not good, but you get the idea

    1 Attachment
  24. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    23pi / 20 , is a bit more than pi , yes?

  25. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    now, we need to get the angle 23pi/20 into the range -pi/2 <= <= pi/2

  26. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    okk...

  27. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    1 Attachment
  28. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    isnt it at a distance pi/2 from it?

  29. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    now, I know the graph of sin is symmetric about pi/2

  30. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so if I find the distance between 23pi/20 and pi/2 , then this is the distance I must go to the left and I will still have the equivalent value of the function

  31. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yup..

  32. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    now, the distance between pi/2 and 23pi/ 20 = (23/20 - 1/2) pi = 13pi/20

  33. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    this means that if I go 13pi/20 units left from pi/2 , then I would be at a point that is a reflection in the line x=pi/2

  34. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ie sin(23pi / 20 ) = sin ( pi/2 - 13pi/20 ) = sin ( -3pi/20 )

  35. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    now, since the angle of the sin function is in the range of the invese sin function

  36. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I can apply sin^-1(sin(x) ) = x

  37. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so our answer is -3pi/20

  38. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    oh..i understand now. thankyou so much=)

  39. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    which can be checked on the calculator , put cal in radian mode , type in " sin^-1(sin(23pi /20) )"

  40. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    with the brackets, and you will get something like -0.47 .... which is equal to -3pi/20

  41. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ya..got it

  42. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.