The expression that is equivalent to the given expression is Sin(11π/6).
The given trigonometric expression is: [tex]Sin \frac{7\pi }{6}[/tex]
[tex]Sin\frac{7\pi }{6}[/tex] can be written as [tex]Sin(\pi +\frac{\pi }{6} )[/tex]
What is the value of Sin(π+θ)?
The value of [tex]Sin(\pi +\theta)[/tex] is [tex]-Sin\theta[/tex].
So, [tex]Sin(\pi +\frac{\pi }{6} )=-Sin\frac{\pi }{6}[/tex]
We know that
[tex]Sin(2\pi -\theta)=-Sin\theta[/tex]
Or, [tex]-Sin\theta=Sin(2\pi -\theta)[/tex]
So, [tex]-Sin\frac{\pi }{6} =Sin(2\pi -\frac{\pi }{6} )[/tex]
[tex]-Sin\frac{\pi }{6} =Sin\frac{11\pi }{6}[/tex]
So, the required expression is [tex]Sin\frac{11\pi }{6}[/tex].
Therefore, the expression that is equivalent to the given expression is Sin(11π/6).
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