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lubasha [3.4K]
1 year ago
11

Find the exact value

Mathematics
1 answer:
Mnenie [13.5K]1 year ago
7 0

By using properties for <em>trigonometric</em> functions and <em>trigonometric</em> expressions, we find that the <em>exact</em> value of the sine of the angle 5π/12 radians is \frac{\sqrt{2+\sqrt{3}}}{2}.

<h3>How to find the exact value of a trigonometric expression</h3>

<em>Trigonometric</em> functions are <em>trascendent</em> functions, these are, that cannot be described algebraically. Herein we must utilize <em>trigonometric</em> formulae to calculate the <em>exact</em> value of a <em>trigonometric</em> function:

\sin \frac{5\pi}{12} = \sqrt{\frac{1 - \cos \frac{5\pi}{6} }{2} }

\sin \frac{5\pi}{12} = \sqrt{\frac{1 + \cos \frac{\pi}{6} }{2} }

\sin \frac{5\pi}{12} = \sqrt{\frac{1 + \frac{\sqrt{3}}{2} }{2} }

\sin \frac{5\pi}{12} =  \sqrt{\frac{2+\sqrt{3}}{4} }

\sin \frac{5\pi}{12} = \frac{\sqrt{2+\sqrt{3}}}{2}

By using properties for <em>trigonometric</em> functions and <em>trigonometric</em> expressions, we find that the <em>exact</em> value of the sine of the angle 5π/12 radians is \frac{\sqrt{2+\sqrt{3}}}{2}.

To learn more on trigonometric functions: brainly.com/question/15706158

#SPJ1

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