Dominate the ABCTE Secondary Math Exam 2025 – Countdown to Math Mastery!

Question: 1 / 400

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

π/4

π/6

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

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π/3

π/2

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