Trigonometry: How To Find The Exact Value Of Sin 2𝜋/3 And Sin 4𝜋/6 Using Special Triangles

sin 2𝜋/3 𝑜𝑟 (4𝜋/6)

√3/2

sin 2𝜋/3 is the sine of the angle formed by rotating a line in the counterclockwise direction from the positive x-axis by 2𝜋/3 radians (or 120 degrees) in standard position.

We can use the special triangles to find the exact value of sin 2𝜋/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 2𝜋/3 is an angle in a 30-60-90 triangle, we can use this ratio to find that sin 2𝜋/3 = √3/2.

Similarly, 4𝜋/6 is also an angle in a 30-60-90 triangle. This time, the ratio of the opposite side to the hypotenuse is √3/2 for the 60-degree angle. So, sin 4𝜋/6 = sin 2𝜋/3 = √3/2.

Therefore, sin 2𝜋/3 = sin 4𝜋/6 = √3/2.

More Answers: