Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

cupcakezz Group Title

2cos^2x + sinx-1=0 a. Explain why this equation cannot be factored. b. Use a trigonometric identity to change the equation into one that can be factored. c. Factor the equation. d. Determine all solutions in the interval 0≤x≤2π.

  • 7 months ago
  • 7 months ago

  • This Question is Closed
  1. cupcakezz Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    @Luigi0210

    • 7 months ago
  2. RaphaelFilgueiras Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1389329041541:dw|

    • 7 months ago
  3. cupcakezz Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    @bagajr ??

    • 7 months ago
  4. cupcakezz Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    can you send some things so I can start looking at it ?? @bagajr

    • 7 months ago
  5. cupcakezz Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    @kc_kennylau

    • 7 months ago
  6. kc_kennylau Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Firstly, be familiarized with this identity: \(\sin^2x+\cos^2x=1\)

    • 7 months ago
  7. kc_kennylau Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Corollary: \(\sin^2x=1-\cos^2x\) and \(\cos^2x=1-\sin^2x\).

    • 7 months ago
  8. kc_kennylau Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    You may want to convert the question into an ordinary quadratic equation.

    • 7 months ago
  9. cupcakezz Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    But why cant it be factored??

    • 7 months ago
  10. cupcakezz Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    @bagajr

    • 7 months ago
  11. kc_kennylau Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    You will know why when you convert the question into an ordinary quadratic equation by changing \(\cos^2x\) to \(1-\sin^2x\).

    • 7 months ago
  12. bagajr Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    a) Because cos^2x and sinx are not the same variable. b) Use the following identity to solve for cos^2x\[\sin^{2}(x)+\cos^{2}(x)=1\]\[\cos^{2}(x) =1-\sin^{2}(x)\]Substitute cos^2x for this new expression.\[2\cos^{2}(x)+\sin(x)-1=0\]\[2[1-\sin^{2}(x)]+\sin(x)-1=0\]\[2-2\sin^{2}(x)+\sin(x)-1=0\]\[-2\sin^{2}(x)+\sin(x)+1=0\]\[2\sin^{2}(x)-\sin(x)-1=0\]c) This isn't necessary, but you can make factoring easier by setting y=sin(x)\[2y^{2}-y-1=0\]\[(2y+1)(y-1)=0\]\[(2\sin(x)+1)(\sin(x)-1)=0\]d) When you multiply two things to get 0, one of those things must be 0.\[2\sin(x)+1=0\]\[\sin(x)-1=0\]Solve both equations to get that sin(x) is -1/2 or 1. Use unit circle to find solutions, which are pi/2, 5pi/4, and 7pi/4. |dw:1389329795828:dw|

    • 7 months ago
  13. cupcakezz Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    @bagajr wow thank you very much !

    • 7 months ago
  14. bagajr Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    No problem, I love helping people with this stuff.

    • 7 months ago
  15. cupcakezz Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    @bagajr could you help me with one more?

    • 7 months ago
  16. bagajr Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    Is it a question about this problem or a different one?

    • 7 months ago
  17. cupcakezz Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    prove: tan^2x(1+1/tan^2x)=1/(1-sin^2x)

    • 7 months ago
  18. cupcakezz Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    @bagajr

    • 7 months ago
  19. cupcakezz Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    @bagajr what is the answer??

    • 7 months ago
  20. bagajr Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    \[\tan^2(x)[1+\frac{1}{\tan^{2}(x)}]=\frac{1}{1-\sin^{2}(x)}\]\[\tan^{2}(x)+1=\frac{1}{\cos^{2}(x)}\]\[\frac{\sin^{2}(x)}{\cos^{2}(x)}+1=\frac{1}{\cos^{2}(x)}\]\[\sin^{2}(x)+\cos^{2}(x)=1\]\[1=1\]

    • 7 months ago
  21. cupcakezz Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    thanks again !

    • 7 months ago
  22. bagajr Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    Sorry it takes so long and you're welcome

    • 7 months ago
  23. cupcakezz Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    its fine, no worries

    • 7 months ago
    • Attachments:

See more questions >>>

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.