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anonymous
 4 years ago
Can anyone help me with sin(x)+sin(5x)=2?
anonymous
 4 years ago
Can anyone help me with sin(x)+sin(5x)=2?

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anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0what is the maximum of sin(x)?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0The max for sin(x) = 1 so the only way the equation can equal 2 is for sin(x) and sin(5x) = 1.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Ok, but is there a way to solve it when not using a deductive method?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0The value for x for sin(x) = 1 would be pi/2 in radians or 90 degrees. Therefore the value of sin(5*pi/2) also equal one and the sum equals two.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I think you could use the identity \[\sin \alpha + \sin \beta = 2\sin0.5(\alpha+\beta)\cos0.5(\alpha+\beta)\] and then set this equal to two. This would give you \[\sin0.5(\alpha+\beta)\cos0.5(\alpha+\beta)\] = 1

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0there are many correct values of x: pi/2, pi/2, 3pi/2, etc etc

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Correct values are (pi/2)+2 k pi.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0@commdoc Typo: you mean sin(A) + sin(B) = 2sin((A+B)/2)cos((AB)/2)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0yes  anytime sin(x) is not 1, you cannot get a solution. anytime sin(x) = 1, then sin(5x) = 1 as well, so you get a solution whenever sin(x)=1.
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