snivvles.com
  • snivvles.com
Find all solutions to the equation. 7 sin^2x - 14 sin x + 2 = -5
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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Nnesha
  • Nnesha
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)
snivvles.com
  • snivvles.com
so \[7y ^{2}-14y+7=0\]?
Nnesha
  • Nnesha
yes right now can you solve for y ?

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

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