A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

Find all solutions to the equation. sin^2 x + sin x = 0

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

    factor the sin^2(x)+sin(x)

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

    there is a sin(x) factor in each term

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

    sin x (sin x + 1) = 0 ?

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

    yes now set both factors equal to 0 sin(x)=0 or sin(x)+1=0

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

    so you have to solve both of those equations sin(x)=0 or sin(x)=-1

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

    sin x = 0 , 2pi sin x = -1 would be x = 3pi/2 ?

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

    what about x=pi or x=0 sin(0)=? sin(pi)=?

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

    i get very confused by the unit circle :/

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

    When you look at the unit circle you are looking for when the y-coordinate is 0 since we are talking about sine cos is the x-coordinate

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

    that is when we are solving sin(x)=0

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

    you already found all the solutions to sin(x)=-1 in the interval [0,2pi]

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

    3pi/2 is the only solution to sin x = -1 ?

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

    sin(x)=0 when x=0,pi,2pi those are the solutions in [0,2pi] There are infinitely many more solutions outside that interval

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

    yes sin(x)=-1 has solution x=3pi/2 only if we are looking at [0,2pi]

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

    As I said though if we aren't restricted to this interval then there are infinitely many solutions.

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

    okay, i understand now.

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

    Your question says to find all the solutions.

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

    so it seems we are restricted to the interval [0,2pi]

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

    what did you notice about the solutions to sin(x)=0 like we had solutions 0pi,1pi,2pi,...continuing this pattern you should be able to say in general the solutions to sin(x)=0 is npi where n is an integer

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

    multiples of 2pi right?

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

    sin(x)=-1 you said had solution x=3pi/2 to include all the solutions you could recall the period of sin is 2pi and say the solutions to sin(x)=-1 are x=3pi/2+2pi*n where again n is an integer

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

    well to the first equation sin(x)=0 the answers are multiples of pi

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

    you say the solution is sin(x)=0 is x=2npi you are excluding odd n..because the 2 in front of the n makes it is even for any n for example x=2npi doesn't include the solution x=pi

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

    so you do have to include all the solutions to sin(x)=0 we say the solutions are x=npi where n is an integer

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

    okay, i see now

  26. 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.