How do you solve $5 {sin}^{2} (α) - 11 sin (α) + 2 = 0$ $5 sin^2 (alpha) - 11 sin (alpha) + 2=0$ ?

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How do you solve $5 {sin}^{2} (α) - 11 sin (α) + 2 = 0$ $5 sin^2 (alpha) - 11 sin (alpha) + 2=0$ ?

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Answer 1 · 2016-08-10T13:03:21

$α = {11.54}^{\circ}$ $alpha=11.54^@$

Explanation:

Let $sin (α) = x$ $sin(alpha)=x$
Hence we can write
$5 x^{2} - 11 x + 2 = 0$ $5x^2-11x+2=0$
or
$5 x^{2} - 10 x - x + 2 = 0$ $5x^2-10x-x+2=0$
or
$5 x (x - 2) - 1 (x - 2) = 0$ $5x(x-2)-1(x-2)=0$
or
$(x - 2) (5 x - 1) = 0$ $(x-2)(5x-1)=0$
or
$x - 2 = 0$ $x-2=0$
or
$x = 2$ $x=2$
or
$5 x - 1 = 0$ $5x-1=0$
or
$5 x = 1$ $5x=1$
or
$x = \frac{1}{5}$ $x=1/5$
or
Out of the above two solutions $sin α = 2$ $sinalpha=2$ which is invalid
Hence
$sin α = \frac{1}{5}$ $sinalpha=1/5$
or
$α = {sin}^{- 1} (\frac{1}{5})$ $alpha=sin^-1(1/5)$
or
$α = {11.54}^{\circ}$ $alpha=11.54^@$

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Explanation:

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