Problem

Find the terminal point on the unit circle determined by $-\frac{11 \pi}{6}$ radians.
Use exact values, not decimal approximations.
\[
(x, y)=\left(\prod, \square\right)
\]

Answer

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Answer

\(\boxed{\text{The terminal point on the unit circle determined by } -\frac{11 \pi}{6} \text{ radians is } \left(\frac{\sqrt{3}}{2}, \frac{1}{2}\right)}\)

Steps

Step 1 :We are given the angle in radians as \(-\frac{11 \pi}{6}\).

Step 2 :We know that the unit circle repeats every \(2\pi\) radians. So, we can add \(2\pi\) to the given angle until we get a positive angle that is less than \(2\pi\).

Step 3 :The terminal point on the unit circle determined by a given angle can be found using the cosine and sine of that angle as the x and y coordinates respectively.

Step 4 :Looking at the decimal approximations, it appears that the x-coordinate corresponds to \(\frac{\sqrt{3}}{2}\) and the y-coordinate corresponds to \(\frac{1}{2}\).

Step 5 :\(\boxed{\text{The terminal point on the unit circle determined by } -\frac{11 \pi}{6} \text{ radians is } \left(\frac{\sqrt{3}}{2}, \frac{1}{2}\right)}\)

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