Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

johnnyalln

  • 2 years ago

Solve by factoring: 2sinxcosx=sinx in [0,2π)

  • This Question is Closed
  1. ganeshie8
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    begin by subtractcting sinx both sides, and then factor sinx

  2. ganeshie8
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \(2\sin x \cos x=\sin x \) subtract sinx both sides \(2 \sin x \cos x - \sin x = 0\) factor out sinx \(\sin x (2 \cos x - 1) = 0 \)

  3. ganeshie8
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    We now have two factors whose product is zero, so the original equation will be satisfied when either factor is zero.

  4. ganeshie8
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    first set first factor = 0 => \(\sin x = 0\) the sin function 0, when \(x = 0 \) or \(x = \pi\) or \(x = 2\pi\)

  5. ganeshie8
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    similarly set the second factor = 0, and try getting other remaining solutions.

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

    I think i get this.. so the final answer would be x=0 or x=pi

  7. ganeshie8
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    not exactly thats half of the solutions only.. you need to set the second factor also equal to 0, and see what solutions u get

  8. ganeshie8
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    set second factor = 0 => \(2 \cos x -1 = 0\) \(\cos x = 1/2\) since, cos is positive in first and fourth quadrants : solution in first quadrant : \(x = \pi/3\) solution in fourth quadrant : \(x = 2\pi - \pi/3 = 5\pi/3\)

  9. ganeshie8
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so, the solutions in interval \([0, 2\pi]\) are : \(0, \ \pi, \ \pi/3, \ 5\pi/3, \ 2\pi\)

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

    Got ya! I just got all of those except for 2pi..

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

    But yes makes perfect sense!

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

    Thanks a lot!

  13. ganeshie8
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1352555743690:dw|

  14. ganeshie8
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    since we are looking for \(\sin x = 0\), we look at the graph of \(\sin\), see that the graph of \(\sin\) is becoming \(0\) when \(x = 0\) or \(x = \pi\) or \(x = 2\pi\) since all these 3 values of x are in the range \([0, 2\pi]\) , all 3 values satisfy the equation, and interval.

  15. ganeshie8
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yw :)

  16. 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.