To find the intersection point of the terminal side of an angle measuring [tex]\(\frac{\pi}{6}\)[/tex] radians with the unit circle, follow these steps:
1. Understand the Unit Circle:
- The unit circle is a circle with a radius of 1 centered at the origin (0,0).
- Any point on the unit circle can be defined as [tex]\((\cos(\theta), \sin(\theta))\)[/tex] where [tex]\(\theta\)[/tex] is the angle measured in radians from the positive x-axis.
2. Use the Given Angle:
- The angle given is [tex]\(\frac{\pi}{6}\)[/tex] radians.
3. Apply Trigonometric Functions:
- For the angle [tex]\(\frac{\pi}{6}\)[/tex]:
- [tex]\(\cos\left(\frac{\pi}{6}\right)\)[/tex] gives the x-coordinate.
- [tex]\(\sin\left(\frac{\pi}{6}\right)\)[/tex] gives the y-coordinate.
4. Evaluate the Trigonometric Values:
- From trigonometry, we know:
- [tex]\(\cos\left(\frac{\pi}{6}\right) = \frac{\sqrt{3}}{2}\)[/tex]
- [tex]\(\sin\left(\frac{\pi}{6}\right) = \frac{1}{2}\)[/tex]
5. Identify the Intersection Point:
- Using the values obtained, the coordinates of the intersection point are:
- [tex]\(\left(\frac{\sqrt{3}}{2}, \frac{1}{2}\right)\)[/tex]
Given this analysis, the correct intersection point of the terminal side of an angle of [tex]\(\frac{\pi}{6}\)[/tex] radians with the unit circle is:
[tex]\[
\left(0.8660254037844387, 0.49999999999999994 \right)
\][/tex]
Thus, the choice corresponding to these values is:
[tex]\[
\left(\frac{\sqrt{3}}{2}, \frac{1}{2}\right)
\][/tex]
