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If sine of the quantity x plus y end quantity equals one half times sine of x plus radical 3 over 2 times cosine of x comma what is the value of y?

If sine of the quantity x plus y end quantity equals one half times sine of x plus-example-1
User Bumbu
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The sine addition formula states that


\sin (a+b)=\sin a\cos b+\cos a\sin b

Thus, in our case,


\sin (x+y)=\sin x\cos y+\cos x\sin y

Then,


\begin{gathered} \Rightarrow\sin x\cos y+\cos x\sin y=(1)/(2)\sin x+\frac{\sqrt[]{3}}{2}\cos x \\ \Rightarrow\cos y=(1)/(2),\sin y=\frac{\sqrt[]{3}}{2} \end{gathered}

Solving for y,


\Rightarrow y=\cos ^(-1)((1)/(2))=(\pi)/(3)

Thus, the answer is y=pi/3

User Jluzwick
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