The unit circle is defined as the set of all points in the Cartesian plane that are at a distance of 1 from the origin (0, 0). The equation for the unit circle is given by:
x² + y² = 1
To find the point (x, y) corresponding to the angle t = 2π/3, we can use the parametric equations of the unit circle:
x = cos(t)
y = sin(t)
Now, substituting t = 2π/3 into these equations, we can calculate the coordinates:
- x = cos(2π/3).
Since 2π/3 is in the second quadrant, where cosine is negative, we find:
- cos(2π/3) = -1/2
y = sin(2π/3).
In the second quadrant, sine is positive, so:
- sin(2π/3) = √3/2
Thus, the coordinates (x, y) on the unit circle that correspond to t = 2π/3 are:
- x = -1/2
- y = √3/2
In conclusion, the point on the unit circle corresponding to the angle t = 2π/3 is (-1/2, √3/2).