Find the coordinates of the point on the unit circle where the angle with the positive x-axis is $45^{circ}$.

Answer 1

To find the coordinates of a point on the unit circle where the angle with the positive x-axis is $45^{\circ}$, we use the fact that the unit circle has a radius of 1 and the coordinates are given by $(\cos \theta, \sin \theta)$ for an angle $\theta$.

For $\theta = 45^{\circ}$:

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

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

Therefore, the coordinates are:

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

Answer 2

The unit circle has a radius of 1, and any point on it can be represented as $(cos heta, sin heta)$ where $ heta$ is the angle with the positive x-axis.

Given $ heta = 45^{circ}$:

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

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

Thus, the coordinates of the point are:

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

Answer 3

In the unit circle, a point at an angle $ heta = 45^{circ}$ has coordinates $(cos 45^{circ}, sin 45^{circ})$. Since:

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

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

The point is:

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

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