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What is the approximate area, in square units, or circle C

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1 answer:

Anestetic [448]3 years ago

7 0

See picture hope it helps

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Answer:

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Step-by-step explanation:

Divide equation $6\sin\left(\dfrac{\pi }{5}x\right)=5$ by 6:

$\sin\left(\dfrac{\pi }{5}x\right)=\dfrac{5}{6}.$

Then

$\dfrac{\pi }{5}x=(-1)^k\arcsin\left(\dfrac{5}{6}\right)+\pi k,\ k\in Z,$

$x=(-1)^k\dfrac{5}{\pi }\arcsin\left(\dfrac{5}{6}\right)+5k,\ k\in Z.$

Since $\arcsin\left(\dfrac{5}{6}\right)\approx 56^{\circ}\approx \dfrac{\pi }{3.2},$

four smallest positive solutions are

1. $\dfrac{5}{3.2}\approx 1.568,\ k=0;$

2. $\dfrac{-5}{3.2}+5\approx 3.432,\ k=1;$

3. $\dfrac{5}{3.2}+10\approx 11.568,\ k=2;$

4. $\dfrac{-5}{3.2}+15\approx 13.432,\ k=3.$

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