Question

what is csc \frac{5\pi}{6}?

Explanation:

Step1: Recall the definition of cosecant

\(\csc\theta=\frac{1}{\sin\theta}\)
So, \(\csc\frac{5\pi}{6}=\frac{1}{\sin\frac{5\pi}{6}}\)

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

We know that \(\sin\frac{5\pi}{6}=\sin(\pi - \frac{\pi}{6})\)
Using the identity \(\sin(\pi-\alpha)=\sin\alpha\), we get \(\sin\frac{5\pi}{6}=\sin\frac{\pi}{6}\)
And \(\sin\frac{\pi}{6}=\frac{1}{2}\)

Step3: Calculate \(\csc\frac{5\pi}{6}\)

Substitute \(\sin\frac{5\pi}{6}=\frac{1}{2}\) into \(\csc\frac{5\pi}{6}=\frac{1}{\sin\frac{5\pi}{6}}\)
\(\csc\frac{5\pi}{6}=\frac{1}{\frac{1}{2}} = 2\)

Answer:

\(2\)