find the exact value. sin\\frac{-5\\pi}{6} type + or -

Explanation:

Step1: Use the property of sine function

We know that (\sin(-\alpha)=-\sin\alpha). So, (\sin\frac{-5\pi}{6}=-\sin\frac{5\pi}{6}).

Step2: Find the value of (\sin\frac{5\pi}{6})

(\frac{5\pi}{6}) is in the second quadrant where sine is positive. And (\sin\frac{5\pi}{6}=\sin(\pi - \frac{\pi}{6})). Using the formula (\sin(\pi-\alpha)=\sin\alpha), we get (\sin(\pi - \frac{\pi}{6})=\sin\frac{\pi}{6}). Since (\sin\frac{\pi}{6}=\frac{1}{2}).

Step3: Calculate the final value

Substitute (\sin\frac{5\pi}{6}=\frac{1}{2}) into (-\sin\frac{5\pi}{6}), we get (-\frac{1}{2}).

Answer:

(-\frac{1}{2})