Identify the sine value of an angle corresponding to $ frac{3pi}{4} $

We start by noting that $ \frac{3\pi}{4} $ is in the second quadrant of the unit circle.

In the second quadrant, the sine value is positive, so we have:

$ \sin \left( \frac{3\pi}{4} \right) = \sin( \pi – \frac{\pi}{4}) = \sin \left( \frac{\pi}{4} \right) $

Since $ \sin \left( \frac{\pi}{4} \right) = \frac{\sqrt{2}}{2} $:

$ \sin \left( \frac{3\pi}{4} \right) = \frac{\sqrt{2}}{2} $

Since $ frac{3pi}{4} $ is in the second quadrant, we know:

$ sin left( frac{3pi}{4}
ight) = sin left( pi – frac{pi}{4}
ight) $

Thus, we have:

$ sin left( frac{3pi}{4}
ight) = sin left( frac{pi}{4}
ight) $

Therefore:

$ sin left( frac{3pi}{4}
ight) = frac{sqrt{2}}{2} $

For $ frac{3pi}{4} $ in the second quadrant:

$ sin left( frac{3pi}{4}
ight) = frac{sqrt{2}}{2} $

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