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galben [10]
3 years ago
12

Is 5.565656... a rational number

Mathematics
2 answers:
seropon [69]3 years ago
7 0

Answer:

Yes 5.565656 is a rational number

Step-by-step explanation:

How do we know?

Rational: Numbers that end and do not go on forever

Examples:

Decimals that end or repeat (in your case)

Fractions

Whole numbers

Square Roots

Kitty [74]3 years ago
5 0

Answer:

Yes

Step-by-step explanation:

A rational number is a number that can be expressed as a fraction. Since the numbers after the decimal are repeating, (it's just repeating 56 over and over) it can be written as a fraction.

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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

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