Answer :
To determine the point of intersection of the terminal side of an angle measuring \(\frac{\pi}{6}\) 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) in the coordinate plane.
2. Determine Cosine and Sine Values for \(\frac{\pi}{6}\):
- The cosine of an angle \(\theta\) on the unit circle represents the x-coordinate of the point of intersection.
- The sine of an angle \(\theta\) on the unit circle represents the y-coordinate of the point of intersection.
3. Calculate the Cosine and Sine for \(\frac{\pi}{6}\):
- \(\cos\left(\frac{\pi}{6}\right)\) gives the x-coordinate.
- \(\sin\left(\frac{\pi}{6}\right)\) gives the y-coordinate.
4. Recall the Known Trigonometric Values:
- \(\cos\left(\frac{\pi}{6}\right) = \frac{\sqrt{3}}{2}\)
- \(\sin\left(\frac{\pi}{6}\right) = \frac{1}{2}\)
5. Combine the Coordinates:
- Thus, the point where the terminal side at \(\frac{\pi}{6}\) radians intersects the unit circle is \(\left(\frac{\sqrt{3}}{2}, \frac{1}{2}\right)\).
Therefore, the point where the terminal side of an angle measuring \(\frac{\pi}{6}\) radians intersects the unit circle is:
[tex]\[ \left(\frac{\sqrt{3}}{2}, \frac{1}{2}\right) \][/tex]
From the given options, the correct answer is:
[tex]\[ \left(\frac{\sqrt{3}}{2}, \frac{1}{2}\right) \][/tex]
1. Understand the Unit Circle:
- The unit circle is a circle with a radius of 1 centered at the origin (0,0) in the coordinate plane.
2. Determine Cosine and Sine Values for \(\frac{\pi}{6}\):
- The cosine of an angle \(\theta\) on the unit circle represents the x-coordinate of the point of intersection.
- The sine of an angle \(\theta\) on the unit circle represents the y-coordinate of the point of intersection.
3. Calculate the Cosine and Sine for \(\frac{\pi}{6}\):
- \(\cos\left(\frac{\pi}{6}\right)\) gives the x-coordinate.
- \(\sin\left(\frac{\pi}{6}\right)\) gives the y-coordinate.
4. Recall the Known Trigonometric Values:
- \(\cos\left(\frac{\pi}{6}\right) = \frac{\sqrt{3}}{2}\)
- \(\sin\left(\frac{\pi}{6}\right) = \frac{1}{2}\)
5. Combine the Coordinates:
- Thus, the point where the terminal side at \(\frac{\pi}{6}\) radians intersects the unit circle is \(\left(\frac{\sqrt{3}}{2}, \frac{1}{2}\right)\).
Therefore, the point where the terminal side of an angle measuring \(\frac{\pi}{6}\) radians intersects the unit circle is:
[tex]\[ \left(\frac{\sqrt{3}}{2}, \frac{1}{2}\right) \][/tex]
From the given options, the correct answer is:
[tex]\[ \left(\frac{\sqrt{3}}{2}, \frac{1}{2}\right) \][/tex]
