Question #400f1

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Question #400f1

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Answer 1 · 2017-03-06T01:42:30

$\frac{\sqrt{2 - \sqrt{3}}}{2}$ $sqrt(2 - sqrt3)/2$

Explanation:

Use unit circle, trig table , and property of complement arcs.
$sin (\frac{11 π}{12}) = sin (- \frac{π}{12} + π) = sin (\frac{π}{12})$ $sin ((11pi)/12) = sin (-pi/12 + pi) = sin (pi/12)$
Evaluate $sin (\frac{π}{12})$ $sin (pi/12)$ by using trig identity:
$2 {sin}^{2} a = 1 - cos 2 a$ $2sin^2 a = 1 - cos 2a$ .
In this case,
$2 {sin}^{2} (\frac{π}{12}) = 1 - cos (\frac{π}{6}) = 1 - \frac{\sqrt{3}}{2} = \frac{2 - \sqrt{3}}{2}$ $2sin^2 (pi/12) = 1 - cos (pi/6) = 1 - sqrt3/2 = (2 - sqrt3)/2$
${sin}^{2} (\frac{π}{12}) = \frac{2 - \sqrt{3}}{4}$ $sin^2 (pi/12) = (2 - sqrt3)/4$
$sin (\frac{π}{12}) = \pm \frac{\sqrt{2 - \sqrt{3}}}{2}$ $sin (pi/12) = +- sqrt(2 - sqrt3)/2$ .
Sine $sin (\frac{π}{12})$ $sin (pi/12)$ is positive, take the positive value.
Finally, $sin (\frac{11 π}{12}) = sin (\frac{π}{12}) = \frac{\sqrt{2 - \sqrt{3}}}{2}$ $sin ((11pi)/12) = sin (pi/12) = sqrt(2 - sqrt3)/2$

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Question #400f1

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