Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

jahvoan

  • one year ago

Solve each equation for 0 = x = 2π : i) 2cos^(2)x + 3cosx – 2 = 0 ii) sinx = sqrt 3cosx (Rewards for correct answer)

  • This Question is Closed
  1. enka
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    did you mean \[ (1)\quad2cos^2x+3cosx−2=0\\ (2)\quad \sin x=\sqrt{3}\cos x\\ \text{for }0\le x \le2\pi\] ???

  2. darkb0nebeauty
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    a. (2cosx-1)(cosx+2)=0 cosx=1/2 or cosx=-2 x={π/3, 5π/6} This is correct, i promise...

  3. ZeHanz
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    If you set p=cos x in the first one, you get: 2p²+3p-2=0. You can solve this, using the quadratic formula. Once you've got you p, remember cos x = p, so solve for x.

  4. darkb0nebeauty
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Do you get mines @jahvoan

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

    i got the answer but what is the corresponding angle for -2 on the unit circle?

  6. ZeHanz
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    There isn't. cosx=-2 has no solutions, because the x-coordinate of a point on the unit circle (which is the cosine) only has values from -1 to 1...

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

    ok thanks

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

    solve equation 2

  9. ZeHanz
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    You can divide both sides by cos x and remember sinx/cosx = tan x

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

    but on the right it is sqrt cosx

  11. ZeHanz
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    No, it's sqrt(3) * cosx

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

    no look at the problem up top

  13. ZeHanz
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    It says: sinx = sqrt 3cosx This can only mean:\[ \sin x = \sqrt{3} \cdot \cos x\]So dividing by cos x gives:\[\frac{ \sin x }{\cos x }=\sqrt{3} \Leftrightarrow \tan x=\sqrt{3}\]And this is a "nice" value of tan x. If you interpret it otherwise, you can't solve it...

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

    so what will be the answer for sqrt 3 on the unit circle?

  15. ZeHanz
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Remember that special triangle with sides of a, 2a and a√3?

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

    is it pi/6

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

    no its pi/3 right or wrong?

  18. ZeHanz
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    60 degrees, or pi/3

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

    thanks mayne

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

    why is equation 2 not considered to be an identity?

  21. ZeHanz
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Identities hold for every x. This one is only true if x = pi/3. Identity: sinx=cos(pi/2-x). No matter what x is, it's always true!

  22. 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.