The sine of pi/6 (or sin(π/6)) is equal to 1/2.
Here's how to understand why:
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Understanding Pi/6: Pi/6 radians is equivalent to 30 degrees.
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Using the Unit Circle: Consider a unit circle (a circle with a radius of 1 centered at the origin). An angle of π/6 (30 degrees) creates a right triangle where:
- The hypotenuse is the radius of the unit circle, which is 1.
- The opposite side to the π/6 angle has a length of 1/2.
- The adjacent side has a length of √3/2.
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Sine Definition: The sine of an angle in a right triangle is defined as the ratio of the length of the opposite side to the length of the hypotenuse.
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Calculation: Therefore, sin(π/6) = (opposite side) / (hypotenuse) = (1/2) / 1 = 1/2.
Therefore, the sin(π/6) = 1/2.
