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Law Incorporation [45]
2 years ago
7

Solve the equation on the interval [0, 27r). 4(sin x)2 - 2 = 0

Mathematics
1 answer:
Ket [755]2 years ago
4 0

4[sin(x)]^2 - 2 = 0\implies 4[sin(x)]^2=2\implies [sin(x)]^2=\cfrac{2}{4}\implies [sin(x)]^2=\cfrac{1}{2} \\\\\\ sin(x)=\pm\sqrt{\cfrac{1}{2}}\implies sin^{-1}[sin(x)]=sin^{-1}\left( \pm\sqrt{\cfrac{1}{2}} \right)\implies x=sin^{-1}\left( \pm\sqrt{\cfrac{1}{2}} \right)

x=sin^{-1}\left( \pm\cfrac{\sqrt{1}}{\sqrt{2}} \right)\implies x=sin^{-1}\left( \pm\cfrac{1}{\sqrt{2}} \right)\implies x=sin^{-1}\left( \pm\cfrac{\sqrt{2}}{2} \right) \\\\[-0.35em] ~\dotfill\\\\ ~\hfill x=\cfrac{\pi }{4}~~,~~\cfrac{3\pi }{4}~~,~~\cfrac{5\pi }{4}~~,~~\cfrac{7\pi }{4}~\hfill

Check the picture below.

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The quotient in polynomial form is C. x² - x ₊ 1.

<h3>What is synthetic division?</h3>

In algebra, synthetic division is a method for manually performing Euclidean division of polynomials, with less calculation than long division.

The given problem is-

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Using synthetic division method,

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So, the remainder from the calculation is 6 .

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