A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

Solve this Equation: sin(x+pi/4)-sin(x-pi/4)=1 I do not just want the answer. I want this explained to me so I understand it. Thank you!

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

    The formula that I would use is the difference formula for sine, right? The difference formula for sin is: sin(a-b)= sina cosb- cosa sinb

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

    @mathmate Please help me! I will award metal???

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

    @hick4life

  4. hick4life
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    ok i got cha

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

    You have the right approach, can you continue? @HaileyJCaroen

  6. hick4life
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    open up" each of the terms, using the definition

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

    Well what I have is =sin(x+pi/4)-sin(x-pi/4) =-2sin(x+pi/4-x+pi/4) cos(x+pi/4-X+pi/4) /2 I don't know if that is right.

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

    well I know that a=x and pi/4=b

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

    So I guess I am supposed to plug in a and b into the difference formula for sine. So that would be: sin(x-pi/4)=sin(x) cos(pi/4)- cos(x) sin(pi/4)

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

    exactly, do the same for both sin(x+pi/4) and sin(x-pi/4), when you add the terms, something magical will happen! :)

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

    What do you mean?

  12. hick4life
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    sin(A+B) = sin (A)* cos (B) + sin (B) cos (A) sin(A-B) = sin (A) * cos (B) - sin (B) cos (A) therefore, sin(x+pi/4)+sin(x-pi/4) = sin(x)cos(pi/4)+sin(pi/4)cos(x) + sin(x)cos(pi/4)-sin(pi/4)cos(x) = 2*sin(x) cos(pi/4) Now, cos(pi/4)=cos(45 degrees) = 1/sqrt(2). Therefore sin(x+pi/4)+sin(x-pi/4)=2*(1/sqrt(2))*... = sqrt(2) * sin(x) and finally, we make this equal to 1: sin(x+pi/4) +sin(x-pi/4) = sqrt(2) sin(x) = 1 therefore the x's that solve this will be: sin(x)=1/sqrt(2) --> x=pi/4, 3pi/4, 9pi/4, 11pi/4, 15pi/4, 17pi/4, and also -7pi/4, -5pi/4, -13pi/4, -15pi/4...etc in general: x= pi/4 (plus minus) 2*pi and x = - pi/4 (plus minus) 2*pi the "plus minus" 2*pi is considering any number of cycles you want to make around the unit circle.

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

    Oh I get it. You use both difference formulas and add them.

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

    Thank you both for helping me! I have a similar question I need help with.

  15. hick4life
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    no problem

  16. 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.