A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

Which of the following are solutions to the equation cos^2 (2x) - 1/4 = 0? Check ALL that apply. A. 5 pi/ 6 B. 11pi / 3 C. pi / 6 D. 12pi / 6

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

    From doing some current calculations. I came to the conclusion of C. Not sure if it is right or if there are anymore answers

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

    \(\large\color{black}{ \displaystyle {\rm Cos}^2 (2x) - \frac{1}{4} = 0 }\) \(\large\color{black}{ \displaystyle {\rm Cos}^2 (2x)= \frac{1}{4} }\) \(\large\color{black}{ \displaystyle \left(~~ {\rm Cos} (2x)~\right)^2= \left(\frac{1}{2}\right)^2 }\)

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

    hope that helps...

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

    (take the square root of both sides, and don't forget the \(\pm\) )

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

    Ok! I will try to solve from there and I'll tell you what I get

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

    sure:)

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

    (oh, there is only 1 incorrect option)

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

    So \[\cos(2x) = \pm \frac{ 1 }{ 2 }\] If I remember how to do this properly, I think I find what 1/2 is on the unit circle, which would be 60? Then divide 60 by 2 and get 30 degrees?

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

    So there are 3 correct answers?

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

    yes

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

    30 degrees is one of them (as you said)

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

    Ok! Now I do not know where to do from here

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

    We already have \[\frac{ \pi }{ 6}\] as one answer

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

    you can plug the rest of the options, if you don't want to go ahead and generate the solution sets for -1/2 and +1/2.

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

    yes π/6 is correct

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

    I don't think I plugged the numbers in properly, but I got 12pi/6 and 5pi/6?

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

    12π/6 is not right

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

    5π/6 is right

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

    Ok! So how would I plug them in? I know I did it wrong haha

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

    (click alt, and hold it click 2 2 7 respectively on your number pad on the left if you have one release alt: you get π)

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

    you would just plug the answer choices instead of x, into that equation cos²(2x)-1/4=0

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

    Oh and what gets you = 0 right?

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

    \[2 \cos ^22x=\frac{ 1 }{ 2 }\] \[1+\cos 4x=\frac{ 1 }{ 2 }\] \[\cos 4x=\frac{ 1 }{ 2 }-1=-\frac{ 1 }{ 2 }=-\cos \frac{ \pi }{ 3 }=\cos \left(2n \pi+ \pi \pm \frac{ \pi }{ 3 } \right)\] where n is an integer. \[4x=\left( 2n+1 \right)\pi \pm \frac{ \pi }{ 3 }\] \[x=\frac{ 1 }{ 4 }\left\{ \left( 2n+1 \right)\pi \pm \frac{ \pi }{ 3 } \right\}\] now you can check by plugging n=0,1,2,....

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

    cos(4x) :) I haven't thought of that one....

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

    So the answers would be \[\frac{ 5\pi }{ 6}, \frac{ 11\pi }{ 3 }, and \frac{ \pi }{ 6 }?\]

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

    yes. use ~ for space

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

    yw

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

    Thank you for your time and the tips :)

  29. 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.