Find the coordinates of the point on the unit circle at an angle of $45^circ$

To find the coordinates of the point on the unit circle at an angle of $45^\circ$, we use the fact that the unit circle has a radius of 1.

The coordinates for an angle $\theta$ in radians can be given by $(\cos \theta, \sin \theta)$.

Converting $45^\circ$ to radians:

$\theta = 45^\circ = \frac{45 \pi}{180} = \frac{\pi}{4}$

Therefore, the coordinates are:

$ (\cos \frac{\pi}{4}, \sin \frac{\pi}{4}) $

Since $\cos \frac{\pi}{4} = \sin \frac{\pi}{4} = \frac{\sqrt{2}}{2}$, the coordinates are:

$ \left( \frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2} \right) $

To find the point on the unit circle at $45^circ$, remember that the unit circle’s radius is 1 and the coordinates are given by $(cos heta, sin heta)$.

First convert $45^circ$ to radians:

$ heta = frac{pi}{4}$

Now we calculate:

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

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

Hence, the coordinates are:

$left( frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight)$

The coordinates at $45^circ$ on a unit circle are:

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

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