sin 2๐/3 ๐๐ (4๐/6)
โ3/2
sin 2๐/3 is the sine of the angle formed by rotating a line in the counterclockwise direction from the positive x-axis by 2๐/3 radians (or 120 degrees) in standard position.
We can use the special triangles to find the exact value of sin 2๐/3. The 30-60-90 triangle tells us that the ratio of the opposite side to the hypotenuse is 1/2 for the 60-degree angle. Since 2๐/3 is an angle in a 30-60-90 triangle, we can use this ratio to find that sin 2๐/3 = โ3/2.
Similarly, 4๐/6 is also an angle in a 30-60-90 triangle. This time, the ratio of the opposite side to the hypotenuse is โ3/2 for the 60-degree angle. So, sin 4๐/6 = sin 2๐/3 = โ3/2.
Therefore, sin 2๐/3 = sin 4๐/6 = โ3/2.
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