Use the special triangle shown on the unit circle to find the sine of
π/3
.
To find the sine of π/3 using the special triangle shown on the unit circle, we look at the y-coordinate of the point on the unit circle corresponding to π/3.
In the special triangle, the side opposite the angle π/3 is the short leg, which has a length of 1/2. The hypotenuse is always 1 in the unit circle.
Since the sine of an angle is equal to the ratio of the length of the opposite leg to the length of the hypotenuse, we have:
sin(π/3) = length of opposite leg / length of hypotenuse
= 1/2 / 1
= 1/2
Therefore, sin(π/3) = 1/2.