The exact value of sin(π/6) is 1/2.
To understand why this is the case, we can refer to the unit circle. The angle π/6 radians, which is equivalent to 30 degrees, corresponds to a point on the unit circle. In the unit circle, the sine function gives the y-coordinate of the point on the circle corresponding to a given angle.
At the angle of π/6, the coordinates of the point on the unit circle are (√3/2, 1/2). Here, the x-coordinate is √3/2, and the y-coordinate is 1/2. Since the sine value is defined as the y-coordinate, we find that:
- sin(π/6) = y-coordinate = 1/2
This method can be very helpful when trying to find exact values of trigonometric functions for common angles.