What are the sine and cosine values of $45^{circ}$ on the unit circle?

First, let’s convert 45 degrees into radians using the conversion factor $\pi / 180$.

$\text{Radians} = 45 \times \frac{\pi}{180} = \frac{\pi}{4}$

On the unit circle, the coordinates corresponding to an angle of $\frac{\pi}{4}$ radians are given by $\left(\cos \frac{\pi}{4}, \sin \frac{\pi}{4}\right)$.

We know that:

$\cos \frac{\pi}{4} = \cos 45^{\circ} = \frac{\sqrt{2}}{2}$

$\sin \frac{\pi}{4} = \sin 45^{\circ} = \frac{\sqrt{2}}{2}$

Therefore, the sine and cosine values for 45 degrees on the unit circle are $\frac{\sqrt{2}}{2}$ and $\frac{\sqrt{2}}{2}$ respectively.

To find the sine and cosine of 45 degrees on the unit circle, we first recall that 45 degrees is equivalent to $frac{pi}{4}$ radians.

$ ext{Radians} = 45 imes frac{pi}{180} = frac{pi}{4}$

On the unit circle, the coordinates corresponding to an angle of $frac{pi}{4}$ radians are:

$cos frac{pi}{4} = cos 45^{circ} = frac{sqrt{2}}{2}$

$sin frac{pi}{4} = sin 45^{circ} = frac{sqrt{2}}{2}$

Thus, the sine and cosine values for 45 degrees are $frac{sqrt{2}}{2}$ and $frac{sqrt{2}}{2}$ respectively.

To determine the sine and cosine values for 45 degrees, convert 45 degrees to radians:

$45 imes frac{pi}{180} = frac{pi}{4}$

Then,

$cos frac{pi}{4} = frac{sqrt{2}}{2}$

$sin frac{pi}{4} = frac{sqrt{2}}{2}$

Thus, both sine and cosine values are $frac{sqrt{2}}{2}$.

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