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The terminal side of an angle measuring [tex]$\frac{\pi}{6}$[/tex] radians intersects the unit circle at what point?

A. [tex]\left(\frac{\sqrt{3}}{2}, \frac{1}{2}\right)[/tex]
B. [tex]\left(\frac{1}{2}, \frac{\sqrt{3}}{2}\right)[/tex]
C. [tex]\left(\frac{\sqrt{3}}{3}, \frac{1}{2}\right)[/tex]
D. [tex]\left(\frac{1}{2}, \frac{\sqrt{3}}{3}\right)[/tex]


Sagot :

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]