Solving sin(x)/sin(x+215) = ab/cd

[tony873004]

This isn't homework, but I can't seem to access the math forum at the moment, so I thought I'd ask here.

Homework Statement

sin(x)/sin(x+215) = ab/cd.
Solve for x

Homework Equations

Is there any property for sin x / sin y so I can simplify this?

 

[LCKurtz]

Your equation has the form sin(x) = bsin(x+a) = bsin(x)cos(a) + bcos(x)sin(a)
= bsin(x)(cos(a) + bsin(a))

sin(x)(1-bcos(a)) = bcos(x)sin(a)
$$\frac{\sin(x)}{\cos(x)}=\tan(x)=\frac{b\sin(a)}{1-b\cos(a)}$$

You can now solve using the inverse tangent function.

 

[tony873004]

Thanks LCKurtz!