A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

Help yet again with Trig! ( i tried it, but stuck at the end): find all possible degree solutions 2 sin ^2 x - 2 sin x -1=0

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

    i tried quadratic formula

  2. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok...what do we have here....

  3. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    quads fine.... what did you get for "u"? 2u^2 -2u -1 = 0 where u = sin(x)

  4. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    2 +- 2sqrt(2) ------------ right? 4

  5. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i probably messes that up in my head lol

  6. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    4 - (4)(2)(-1) 12 = 4*3 2sqrt(3) is better

  7. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    (1/2) +- sqrt(3)/2 right?

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

    yes

  9. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    sin(x) = (1/2) + sqrt(3)/2 sin(x) = sin(30) + cos(30) it looks like

  10. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    and sin(x) = sin(30) - sin(60)

  11. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    sin...cos....keep em straight!! lol

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

    You need all degree solutions, yeah, not just over a fixed interval?

  13. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    sin(x) = 2cos(30) but i might have done it in error

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

    In general, \[\theta = n.180^o+(-1)^n \alpha^o\]where \[\alpha^o\]is a seed angle and\[n \in \mathbb{Z}\]You have the seed from the solution to the quadratic, \[\alpha^o = \sin^{-1}\left( \frac{1-\sqrt{3}}{2} \right)\]You have to reject the other solution since arcsine is not defined for an argument outside magnitude 1. So your solution should be,\[\theta =180^o+(-1)^n \sin^{-1}\left( \frac{1-\sqrt{3}}{2} \right)^o\] for n an integer.

  15. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    338.51 degrees and 201.47 degrees are the 2 angles that would produce the proper sin(x) value.... right? then we add k2pi periods to those toget all the values....maybe :)

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

    Sorry, in my last result, there's a typo. It should read:\[\theta = n.180^o+(-1)^n \sin ^ {-1} \left( \frac{1-\sqrt{3}}{2} \right)\]

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

    Yeah, amstre, you're on the right track.

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

    sorry, about late response, but thank you for helping me

  19. 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.