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

1. anonymous

what is the maximum of sin(x)?

2. anonymous

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

3. anonymous

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

4. anonymous

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.

5. anonymous

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

6. anonymous

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

7. anonymous

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

8. anonymous

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

9. anonymous

k is integer.

10. anonymous

Thanks anyway.

11. anonymous

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.

12. anonymous

yeah thanks BF