Convert the point on the unit circle given in Cartesian coordinates $(sqrt{3}/2, 1/2)$ to its corresponding angle in degrees and radians, and verify the solution by converting the angle back to Cartesian coordinates.

We are given the point $(\sqrt{3}/2, 1/2)$ on the unit circle. To find the corresponding angle, we use the following trigonometric relationships:

$x = \cos(\theta)$

$y = \sin(\theta)$

Thus, we have:

$\cos(\theta) = \sqrt{3}/2$

$\sin(\theta) = 1/2$

For the angle $\theta$ that satisfies these equations, we recognize that these are standard values. The angle $\theta$ is $30^{\circ}$ or $\pi/6$ radians.

To verify, we will convert $30^{\circ}$ back to Cartesian coordinates:

$\cos(30^{\circ}) = \sqrt{3}/2, \sin(30^{\circ}) = 1/2$

Thus, the point $(\cos(30^{\circ}), \sin(30^{\circ})) = (\sqrt{3}/2, 1/2)$ matches the given point. Therefore, $\theta = 30^{\circ}$ or $\pi/6$ radians.

Given the point $(sqrt{3}/2, 1/2)$ on the unit circle, we find the corresponding angle using the relationships:

$cos( heta) = sqrt{3}/2$

$sin( heta) = 1/2$

Since $cos( heta)$ and $sin( heta)$ match the values at $ heta = pi/6$, the angle is $30^{circ}$ or $pi/6$ radians.

We verify by converting $pi/6$ back to Cartesian coordinates:

$cos(pi/6) = sqrt{3}/2, sin(pi/6) = 1/2$

The point $(cos(pi/6), sin(pi/6)) = (sqrt{3}/2, 1/2)$ matches. Therefore, $ heta = 30^{circ}$ or $pi/6$ radians.

Given $(sqrt{3}/2, 1/2)$, we find:

$cos( heta) = sqrt{3}/2$

$sin( heta) = 1/2$

These are at $ heta = pi/6$. Checking Cartesian coordinates gives $(sqrt{3}/2, 1/2)$. Hence, $ heta = 30^{circ}$ or $pi/6$ radians.

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