To find \( \cos \theta = \frac{\sqrt{3}}{2} \) on the unit circle, we look for an angle where the cosine value corresponds to that ratio. On the unit circle, cosine represents the x-coordinate of a point.
The angle \( \theta \) that satisfies \( \cos \theta = \frac{\sqrt{3}}{2} \) is \( 30^\circ \) or \( \frac{\pi}{6} \) radians. The reference triangle for this angle is a \( 30^\circ - 60^\circ - 90^\circ \) triangle, where:
- The side opposite the \( 30^\circ \) angle is \(\frac{1}{2}\).
- The side opposite the \( 60^\circ \) angle is \(\frac{\sqrt{3}}{2}\).
- The hypotenuse (which is the radius of the unit circle) is \( 1 \).
Thus, the correct type of triangle to use is the 30 - 60 - 90 triangle.
The correct answer is: a horizontal ray from the origin 30 - 60 - 90 triangle.
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