How do you evaluate sin(pi/6) ?

2 Answers
George C.
Jan 11, 2018

sin(pi/6) = 1/2

Explanation:

Start with an equilateral triangle of side 2. The interior angle at each vertex must be pi/3 since 6 such angles make up a complete 2pi circle.

Then bisect the triangle through a vertex and the middle of the opposite side, dividing it into two right angled triangles.

These will have sides of length 2, 1 and sqrt(2^2-1^2) = sqrt(3). The interior angles of each right angled triangle are pi/3, pi/6 and pi/2, with the pi/6 coming from the fact that we have bisected one of the pi/3 angles.

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Then:

sin(pi/6) = "opposite"/"hypotenuse" = 1/2

Nghi N
Jan 12, 2018

sin (pi/6) = 1/2

Explanation:

Use Half Angle Identity
sin (t/2) = +- sqrt((1 - cos t)/2)
In this case, cos t = cos (pi/3) = 1/2 -->
sin (pi/6) = sqrt((1 - 1/2)/2) = sqrt(1/4) = 1/2

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