Sin and Cos

[Esmaeil]

Hi
How can I solve sin x=sin(x+pi/4)

 

[Deleted member 4993]

Hi
How can I solve sin x=sin(x+pi/4)

Did you post a correct problem?

 

[Dr.Peterson]

If two angles have the same sine (sina = sinb), what relationships might there be between them? They could be the same angle (a=b); or what else?

 

[pka]

How can I solve sin x=sin(x+pi/4)

Here is a second (I think) approach. I would use \(\displaystyle \sin(\alpha+\beta)=\sin(\alpha)\cos(\beta)+\sin(\beta)\cos(\alpha)\)
It is worth noting that \(\displaystyle \sin\left(\frac{\pi}{4}\right)=\cos\left(\frac{\pi}{4}\right)=\frac{\sqrt{2}}{2}\).
Use the \(\displaystyle \arctan\) function to solve for \(\displaystyle x\).

 

[MarkFL]

Another approach would be to arrange the equation as:

[MATH]\sin\left(x+\frac{\pi}{4}\right)-\sin(x)=0[/MATH]
Apply a sum-to-product identity:

[MATH]2\sin\left(\frac{\pi}{8}\right)\cos\left(x+\frac{\pi}{8}\right)=0[/MATH]
[MATH]\cos\left(x+\frac{\pi}{8}\right)=0[/MATH]
What does this imply?

 

[Esmaeil]

I solve it
Thank you so match

 

[MarkFL]

I solve it
Thank you so match

I'm glad to hear it! Would you care to post what you did to solve it and what your answer is?