Find the coordinates of a point on the unit circle where the angle is $45^circ$.

To find the coordinates of a point on the unit circle at an angle of $45^\circ$, we can use the unit circle properties.

The coordinates $(x, y)$ of a point on the unit circle at an angle $\theta$ are given by:

$x = \cos(\theta)$

$y = \sin(\theta)$

For $\theta = 45^\circ$:

$x = \cos(45^\circ) = \frac{\sqrt{2}}{2}$

$y = \sin(45^\circ) = \frac{\sqrt{2}}{2}$

So, the coordinates are:

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

For an angle of $45^circ$ on the unit circle, we can determine the coordinates $(x, y)$ by using the cosine and sine values of the angle.

Using the formulas:

$x = cos( heta)$

$y = sin( heta)$

With $ heta = 45^circ$:

$x = cos(45^circ) = frac{1}{sqrt{2}}$

$y = sin(45^circ) = frac{1}{sqrt{2}}$

Therefore, the coordinates are:

$left( frac{1}{sqrt{2}}, frac{1}{sqrt{2}}
ight)$

For $45^circ$ on the unit circle:

$cos(45^circ) = frac{sqrt{2}}{2}$

$sin(45^circ) = frac{sqrt{2}}{2}$

So the coordinates are:

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

Start Using PopAi Today