anonymous
  • anonymous
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!
Mathematics
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anonymous
  • anonymous
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!
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
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
anonymous
  • anonymous
@mathmate Please help me! I will award metal???
anonymous
  • anonymous

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hick4life
  • hick4life
ok i got cha
mathmate
  • mathmate
You have the right approach, can you continue? @HaileyJCaroen
hick4life
  • hick4life
open up" each of the terms, using the definition
anonymous
  • anonymous
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.
anonymous
  • anonymous
well I know that a=x and pi/4=b
anonymous
  • anonymous
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)
mathmate
  • mathmate
exactly, do the same for both sin(x+pi/4) and sin(x-pi/4), when you add the terms, something magical will happen! :)
anonymous
  • anonymous
What do you mean?
hick4life
  • hick4life
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.
anonymous
  • anonymous
Oh I get it. You use both difference formulas and add them.
anonymous
  • anonymous
Thank you both for helping me! I have a similar question I need help with.
hick4life
  • hick4life
no problem

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