The value of sin 120 degrees is √3/2 or approximately 0.866. There are different methods to derive this value, including:
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Using the unit circle: By constructing an angle of 120 degrees with the x-axis, we can find the value of sin 120 degrees. Since the value of sin 60 degrees is equal to the value of sin 120 degrees, we can use the fact that sin 60 degrees is √3/2 to determine that sin 120 degrees is also √3/2.
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Using other trigonometric angles: We can use the trigonometric identity sin (180°- a ) = sin a to find that sin 120 degrees is equal to sin 60 degrees. Since the value of sin 60 degrees is √3/2, we can conclude that sin 120 degrees is also √3/2.
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Using cosine functions: With the help of the trigonometry formula, sin (90 + a) = cos a, we can find that sin 120 degrees is equal to cos 30 degrees. Since the value of cos 30 degrees is √3/2, we can conclude that sin 120 degrees is also √3/2.
Therefore, the value of sin 120 degrees is √3/2 or approximately 0.866.
