Find all solutions to the equation. 7 sin^2x - 14 sin x + 2 = -5

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Find all solutions to the equation. 7 sin^2x - 14 sin x + 2 = -5

Mathematics
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let sinx = y \[\huge\rm 7y^2-14y+2=-5\] now you have quadratic equation set it equal to zero (move -5 to the left side)
so \[7y ^{2}-14y+7=0\]?
yes right now can you solve for y ?

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Other answers:

\[\frac{ 14+-\sqrt{196-4(7)(7)} }{ 2(7) }\]
oh wait you can take out the common factor
\[\huge\rm 7y ^{2}-14y+7=0\] what is gcf ?
7 so \[\frac{ 2+-\sqrt{4-4} }{ 2 }\]
right!
so \[\frac{ 2 }{ 2 }\]
then I find where that happens on the unit circle, right?
but it simplifies to \[\frac{ 1 }{ 1 }\]
yes right so \[\large\rm \frac{ 2 +0 }{ 2} ~and~ \frac{ 2-0 }{ 2 }\] both equal to one y= 1 now you can replace y with sinx sin x =1 sin x =1
so \[\frac{ \pi }{ 2 }\]
right?
find `all solution`
wait do you need in radians or degree ?
so 3pi/2 5pi/2 7pi/2 etc. ?
radians
yes pi /2 is right !
is 3pi/2 right?
sinx = positive one
oh right so is 5pi/2 right?
so like pi/2 5pi/2 9pi/2 etc.
right?
yes 5pi/2 can be the solutions
Ok, thanks!
but remember sinx =1 (multiplicity of 2)(sinx= 1 , sinx =1)
np good job!
OK!

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