Find the sine and cosine values for $ frac{5pi}{4} $ on the unit circle

To find the sine and cosine values for $ \frac{5\pi}{4} $ on the unit circle, we need to locate the angle on the unit circle. The angle $ \frac{5\pi}{4} $ is in the third quadrant.

In the third quadrant, both the sine and cosine values are negative.

The reference angle for $ \frac{5\pi}{4} $ is $ \frac{\pi}{4} $.

From the unit circle, we know that:

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

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

Thus, the sine and cosine values for $ \frac{5\pi}{4} $ are:

$ \sin\left( \frac{5\pi}{4} \right) = -\frac{\sqrt{2}}{2} $

$ \cos\left( \frac{5\pi}{4} \right) = -\frac{\sqrt{2}}{2} $

To find the sine and cosine values for $ frac{5pi}{4} $ on the unit circle:

The angle $ frac{5pi}{4} $ lies in the third quadrant where both sine and cosine are negative.

Reference angle: $ frac{pi}{4} $

$ sinleft( frac{5pi}{4}
ight) = -frac{sqrt{2}}{2} $

$ cosleft( frac{5pi}{4}
ight) = -frac{sqrt{2}}{2} $

$ frac{5pi}{4} $ is in the third quadrant:

$ sinleft( frac{5pi}{4}
ight) = -frac{sqrt{2}}{2} $

$ cosleft( frac{5pi}{4}
ight) = -frac{sqrt{2}}{2} $

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