Question

Can anyone help me with sin(x)+sin(5x)=2?

Answer 1

what is the maximum of sin(x)?

Answer 2

The max for sin(x) = 1 so the only way the equation can equal 2 is for sin(x) and sin(5x) = 1.

Answer 3

Ok, but is there a way to solve it when not using a deductive method?

Answer 4

The 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.

Answer 5

I 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

Answer 6

there are many correct values of x: pi/2, -pi/2, 3pi/2, etc etc

Answer 7

Correct values are (pi/2)+2 k pi.

Answer 8

@commdoc Typo: you mean sin(A) + sin(B) = 2sin((A+B)/2)cos((A-B)/2)

Answer 9

k is integer.

Answer 10

Thanks anyway.

Answer 11

yes - 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.

Answer 12

yeah thanks BF