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

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SUMMARY

The equation sin(x)/sin(x+215) = ab/cd can be simplified using trigonometric identities. By applying the identity sin(x) = bsin(x+a) = bsin(x)cos(a) + bcos(x)sin(a), the equation can be transformed into sin(x)(1-bcos(a)) = bcos(x)sin(a). This leads to the conclusion that tan(x) = bsin(a)/(1-bcos(a)), allowing for the solution of x using the inverse tangent function.

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tony873004
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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?
 
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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)
[tex]\frac{\sin(x)}{\cos(x)}=\tan(x)=\frac{b\sin(a)}{1-b\cos(a)}[/tex]

You can now solve using the inverse tangent function.
 
Thanks LCKurtz!
 

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