Which common angle corresponds to the coordinates (√3/2, 1/2) on the unit circle?

Which common angle corresponds to the coordinates (√3/2, 1/2) on the unit circle?

• A. π/4
• B. π/6
• C. π/3
• D. π/2

Answer: (B)

The coordinates (√3/2, 1/2) on the unit circle represent a specific angle defined by the cosine and sine values of that angle. In this case, the x-coordinate corresponds to the cosine of the angle, and the y-coordinate corresponds to the sine of the angle. To find the angle, one can refer to the commonly known sine and cosine values of common angles in the unit circle: - The cosine value (x-coordinate) of √3/2 corresponds to the angle where the adjacent side (cosine) in a right triangle has this relationship to the hypotenuse. - The sine value (y-coordinate) of 1/2 similarly denotes the opposite side's length in relation to the triangle's hypotenuse. Focusing specifically on common angles, we see that: - The angle π/6 (or 30 degrees) has a cosine of √3/2 and a sine of 1/2. Therefore, the coordinates (√3/2, 1/2) correspond to π/6, making that the correct angle associated with these coordinates on the unit circle. Other options, such as π/4 and π/3, have different sine and cosine values, while π

The coordinates (√3/2, 1/2) on the unit circle represent a specific angle defined by the cosine and sine values of that angle. In this case, the x-coordinate corresponds to the cosine of the angle, and the y-coordinate corresponds to the sine of the angle.

To find the angle, one can refer to the commonly known sine and cosine values of common angles in the unit circle:

• The cosine value (x-coordinate) of √3/2 corresponds to the angle where the adjacent side (cosine) in a right triangle has this relationship to the hypotenuse.

• The sine value (y-coordinate) of 1/2 similarly denotes the opposite side's length in relation to the triangle's hypotenuse.

Focusing specifically on common angles, we see that:

• The angle π/6 (or 30 degrees) has a cosine of √3/2 and a sine of 1/2.

Therefore, the coordinates (√3/2, 1/2) correspond to π/6, making that the correct angle associated with these coordinates on the unit circle. Other options, such as π/4 and π/3, have different sine and cosine values, while π