Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Christos

  • one year ago

WHERE IS MY MISTAKE?!?!? Problem: Given that sinƟ = 2/3 and Π/2 < Ɵ < Π find the exact value of cosƟ My solution: cos^2(Ɵ) + sin^2(Ɵ) = 1 sin^2(Ɵ) = 1 - cos^2(Ɵ) 4/9=1- cos^2(Ɵ) -5/9 = -cos^2(Ɵ) 5/9 = cos^2(Ɵ) cos(Ɵ) = -sqrt(5/9) Where is my mistake till now?

  • This Question is Closed
  1. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    for one thing, the square root of 9 is 3

  2. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    so if you were typing in an answer, it probably wanted it to look like \[\cos(\theta)=-\frac{\sqrt{5}}{3}\]

  3. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    other than that, it is all correct

  4. Christos
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @satellite73 So I didnt make any mistakes at all?

  5. geerky42
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    No.

  6. Christos
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @satellite73 confirm to me please if all of my steps above were correct, and even if they had a mistake which line?

  7. babycry
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    just draw a triangle and with 0 = 2 and h = 3.. then find a then do a/h to get cos theta

  8. Grazes
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1362625931832:dw|

  9. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    there is no mistake, although you should have \[\pm\sqrt{1-\left(\frac{2}{3}\right)^2}=\cos(\theta)\]

  10. Christos
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I should have used another fundamental identity?

  11. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    or if you write \[\frac{5}{9}=\cos^2(\theta)\] then \[\pm\frac{\sqrt{5}}{3}=\cos(\theta)\] the reason you know it is negative is because you are in quadrant 2

  12. Christos
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    got it its the same just modified, meeh

  13. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    it is right, everything you did is right

  14. Christos
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I know why its negative yea

  15. Christos
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    problem is that My solution is different from the one on the book

  16. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    so there is no mistake here, although you should have a 3 in the denominator, rather than the square root of 9

  17. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    what did the book get?

  18. Christos
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    They the solutions might be equal but, I sill found a different solution

  19. Christos
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    5/9

  20. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    a different solution, or a different method

  21. Christos
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yea right..

  22. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    nothing wrong with your method answer is \(-\frac{\sqrt{5}}{3}\) for sure

  23. Christos
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Books solution: 5/9

  24. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    no that is \(\cos^2(\theta)\)

  25. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    or else the book made a mistake it happens in any case you are right for sure, so don't fret about it

  26. Christos
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    what do you mean "no that is cos2(θ)" ?

  27. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    \[\cos(\theta)=-\frac{\sqrt{5}}{3}\] \[\cos^2(\theta)=\frac{5}{9}\]

  28. Christos
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    hmmmmm

  29. Christos
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Is there any other method to approche the situation, like another identity to use for the specidif prob

  30. Christos
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I AM SORRY the answer in my book was: -sqrt(5)/3 !!!!!

  31. babycry
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1362626751880:dw|

  32. Christos
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So my final outcome is - sqrt(5)/sqrt3 HOW DO I PROCEED?

  33. Christos
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @satellite73

  34. Christos
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @Hero

  35. Christos
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @Mertsj

  36. Christos
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    SOLVED THANK YOU ALL, SPECIAL THANKS TO SATELITE

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

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

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.