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

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The formula that I would use is the difference formula for sine, right? The difference formula for sin is: sin(ab)= sina cosb cosa sinb

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@mathmate Please help me! I will award metal???

mathmate
 one year ago
Best ResponseYou've already chosen the best response.0You have the right approach, can you continue? @HaileyJCaroen

hick4life
 one year ago
Best ResponseYou've already chosen the best response.2open up" each of the terms, using the definition

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Well what I have is =sin(x+pi/4)sin(xpi/4) =2sin(x+pi/4x+pi/4) cos(x+pi/4X+pi/4) /2 I don't know if that is right.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0well I know that a=x and pi/4=b

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So I guess I am supposed to plug in a and b into the difference formula for sine. So that would be: sin(xpi/4)=sin(x) cos(pi/4) cos(x) sin(pi/4)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.0exactly, do the same for both sin(x+pi/4) and sin(xpi/4), when you add the terms, something magical will happen! :)

hick4life
 one year ago
Best ResponseYou've already chosen the best response.2sin(A+B) = sin (A)* cos (B) + sin (B) cos (A) sin(AB) = sin (A) * cos (B)  sin (B) cos (A) therefore, sin(x+pi/4)+sin(xpi/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(xpi/4)=2*(1/sqrt(2))*... = sqrt(2) * sin(x) and finally, we make this equal to 1: sin(x+pi/4) +sin(xpi/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
 one year ago
Best ResponseYou've already chosen the best response.0Oh I get it. You use both difference formulas and add them.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thank you both for helping me! I have a similar question I need help with.
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