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3 years ago

Find the exact area of a circle having the given circumference.

Mathematics

1 answer:

blagie [28]3 years ago

3 0

Answer:

Step-by-step explanation:

The formula of an area of a circle:

$A=\pi r^2$

r - radius

The formula of a circumference of a circle:

$C=2\pi r$

We have:

$C=3\pi$

Substitute:

$2\pi r=3\pi$ divide both sides by 2π

$r=1.5$

Substitute:

$A=\pi(1.5)^2=2.25\pi$

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Answer:

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Step-by-step explanation:

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BlackZzzverrR [31]

Answer:

The solution of the given trigonometric equation

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Step-by-step explanation:

Step(i):-

Given

$cos( 3x - \frac{\pi }{3} ) = \frac{\sqrt{3} }{2}$

$cos( 3x - \frac{\pi }{3} ) = cos (\frac{\pi }{6} )$

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$3x = \frac{2\pi +\pi }{6} = \frac{3\pi }{6} = \frac{\pi }{2}$

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Step(ii):-

The solution of the given trigonometric equation

$x = \frac{\pi }{6}$

verification :-

$cos( 3x - \frac{\pi }{3} ) = \frac{\sqrt{3} }{2}$

put $x = \frac{\pi }{6}$

$cos( 3(\frac{\pi }{6}) - \frac{\pi }{3} ) = \frac{\sqrt{3} }{2}$

$cos (\frac{\pi }{6} ) = \frac{\sqrt{3} }{2} \\\\\frac{\sqrt{3} }{2} = \frac{\sqrt{3} }{2}$

Both are equal

∴The solution of the given trigonometric equation

$x = \frac{\pi }{6}$

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