Find the sine and cosine of the angle $ heta$ on the unit circle when $ heta = frac{5pi}{4}$

To find the sine and cosine of the angle $\theta = \frac{5\pi}{4}$ on the unit circle, we use the definitions of the trigonometric functions on the unit circle. The angle $\frac{5\pi}{4}$ is in the third quadrant.

For angles in the third quadrant, both sine and cosine are negative. The reference angle for $\theta = \frac{5\pi}{4}$ is $\frac{\pi}{4}$.

The sine and cosine of $\frac{\pi}{4}$ are both $\frac{\sqrt{2}}{2}$.

Thus:

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

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

To determine the sine and cosine of $ heta = frac{5pi}{4}$:

Recognize that $ heta = frac{5pi}{4}$ is an angle in the third quadrant, where sine and cosine are negative.

The reference angle is $frac{pi}{4}$, and:

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

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

For $ heta = frac{5pi}{4}$, an angle in the third quadrant:

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

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

Start Using PopAi Today