Question

find the exact value. sin\frac{-3\pi}{2

Explanation:

Step1: Use the property of sine function

The sine function has the property \(\sin(-\alpha)=-\sin\alpha\). So, \(\sin\frac{-3\pi}{2}=-\sin\frac{3\pi}{2}\).

Step2: Find the value of \(\sin\frac{3\pi}{2}\)

We know that on the unit - circle, for an angle \(\theta=\frac{3\pi}{2}\), the coordinates of the point on the unit - circle are \((0, - 1)\). And by the definition of the sine function \(\sin\theta = y\) (where \((x,y)\) is the point on the unit - circle corresponding to the angle \(\theta\)). So, \(\sin\frac{3\pi}{2}=-1\).

Step3: Calculate the value of \(\sin\frac{-3\pi}{2}\)

Since \(\sin\frac{-3\pi}{2}=-\sin\frac{3\pi}{2}\) and \(\sin\frac{3\pi}{2}=-1\), then \(\sin\frac{-3\pi}{2}=-(-1)\).

Answer:

\(1\)