Given a point $P$ on the unit circle at an angle $ heta$, find the coordinates of $P$, the length of the line segment from $P$ to the origin, and the area of the sector formed by the angle $ heta$ in the unit circle.

Given a point $P$ on the unit circle at an angle $\theta$, we can determine the coordinates of $P$ as follows:

$ P(\cos(\theta), \sin(\theta)) $

The length of the line segment from $P$ to the origin is simply the radius of the unit circle, which is 1.

To find the area of the sector formed by the angle $\theta$, we use the formula for the area of a sector, $ A = \frac{1}{2} r^2 \theta $ Since the radius $r$ is 1,

$ A = \frac{1}{2} \theta $

Therefore, the coordinates of $P$ are $(\cos(\theta), \sin(\theta))$, the length of the line segment from $P$ to the origin is 1, and the area of the sector is $\frac{1}{2} \theta$.

For a point $P$ on the unit circle at an angle $ heta$, the coordinates of $P$ are:

$P(cos( heta), sin( heta))$

The length of the line segment from $P$ to the origin is the radius of the unit circle, which is 1.

To find the area of the sector formed by the angle $ heta$, we use the sector area formula:

$A = frac{1}{2} r^2 heta$ With $r = 1$,

$A = frac{1}{2} heta$

Thus, the coordinates of $P$ are $(cos( heta), sin( heta))$, the length of the line segment from $P$ to the origin is 1, and the area of the sector is $frac{1}{2} heta$.

Given a point $P$ on the unit circle at an angle $ heta$:

$ P(cos( heta), sin( heta)) $

Length of the segment from $P$ to the origin: 1

Area of the sector: $ frac{1}{2} heta $

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