How do I evaluate sin(pi/3) without using a calculator?

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Answer 1 · 2015-08-29T16:55:23

$sin(pi/3) = sqrt(3)/2$

Consider the series of diagrams below.

The interior angles of a triangle always add up to $pi$ radians

An equilateral triangle will have all three angles $= pi/3$ and all three sides of equal length.

If we set the sides of the equilateral triangle to $2$ we can avoid fractions when we divide the triangle into 2 halves vertically,

By the Pythagorean Theorem, the height (the side opposite the angle of $pi/3$ ) will have a length of $sqrt(3)$

$sin(pi/3) = ("side opposite "pi/3)/("hypotenuse")=sqrt3/2$

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