To determine the point where the terminal side of an angle measuring [tex]\(\frac{\pi}{6}\)[/tex] radians intersects the unit circle, we need to evaluate the cosine and sine of [tex]\(\frac{\pi}{6}\)[/tex].
1. Understanding the Angle:
- [tex]\(\frac{\pi}{6}\)[/tex] radians corresponds to 30 degrees in the unit circle.
2. Cosine and Sine Values:
- The value of [tex]\(\cos(\frac{\pi}{6})\)[/tex] is [tex]\(\frac{\sqrt{3}}{2}\)[/tex].
- The value of [tex]\(\sin(\frac{\pi}{6})\)[/tex] is [tex]\(\frac{1}{2}\)[/tex].
3. Intersection Point:
- The coordinates of the point where the terminal side of the angle intersects the unit circle are [tex]\((\cos(\frac{\pi}{6}), \sin(\frac{\pi}{6}))\)[/tex].
- Plugging in the values:
[tex]\[
(\cos(\frac{\pi}{6}), \sin(\frac{\pi}{6})) = \left(\frac{\sqrt{3}}{2}, \frac{1}{2}\right)
\][/tex]
4. Choosing the Correct Answer:
- We compare this point with the provided multiple choices:
- [tex]\(\left(\frac{\sqrt{3}}{2}, \frac{1}{2}\right)\)[/tex]
- [tex]\(\left(\frac{1}{2}, \frac{\sqrt{3}}{2}\right)\)[/tex]
- [tex]\(\left(\frac{\sqrt{3}}{3}, \frac{1}{2}\right)\)[/tex]
- [tex]\(\left(\frac{1}{2}, \frac{\sqrt{3}}{3}\right)\)[/tex]
5. Conclusion:
- The correct point is [tex]\(\left(\frac{\sqrt{3}}{2}, \frac{1}{2}\right)\)[/tex].
Thus, the terminal side of an angle measuring [tex]\(\frac{\pi}{6}\)[/tex] radians intersects the unit circle at the point [tex]\(\left(\frac{\sqrt{3}}{2}, \frac{1}{2}\right)\)[/tex], which corresponds to the first choice.
