Question

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?

Answer 1

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