Answer:
The exact value of the sine of pi over 3 is a) ({√{3}}/{2}), which is the ratio of the opposite side to the hypotenuse in a 30°-60°-90° right triangle.
Step-by-step explanation:
The exact value of the sine of pi over 3 is √3/2, which is the ratio of the opposite side to the hypotenuse in a 30°-60°-90° right triangle.
The exact sine value of the quantity pi over 3, often expressed as sin(π/3), is √3/2. We can obtain this value by considering the unit circle or an equilateral triangle divided into two right-angle triangles, each having angles 30°, 60°, and 90°. In such a triangle, the side opposite the 60° angle (corresponding to π/3 radians) is √3 times shorter than the hypotenuse. Therefore, the sine of π/3, the ratio of the length of the opposite side to the hypotenuse is √3/2.
So, the correct answer from the provided options is (a)({√{3}}/{2})
