anonymous
  • anonymous
Find all solutions to the equation. 7 sin^2(x) - 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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Atsie
  • Atsie
https://www.wolframalpha.com/input/?i=7+sin%5E2%28x%29+-+14+sin+x+%2B+2+%3D+-5 I don't know if that will be of any help, but there you go
freckles
  • freckles
this is a quadratic in terms of sin(x)
freckles
  • freckles
Do you know how to solve the following for u: \[7u^2-14u+2=-5\]

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More answers

anonymous
  • anonymous
bring five over and equal it to zero?
anonymous
  • anonymous
7u^2-14u-3??
freckles
  • freckles
but 2+5 is 7 not -3
freckles
  • freckles
\[7u^2-14u+2=-5 \\ \text{ add 5 on both sides } \\ 7u^2-14u+2+5=-5+5 \\ 7u^2-14u+7=0\]
anonymous
  • anonymous
oo ok so now do we combine 7u^2 with 14u?
freckles
  • freckles
you can't they aren't like terms
freckles
  • freckles
have you ever solved a quadratic before
freckles
  • freckles
you can try factoring or use the quadratic formula....or completing the square
anonymous
  • anonymous
ok lets do quadratic form is A=7u^2 and b=14U and c=7 ?
freckles
  • freckles
do you mean a=7, b=-14,c=7 ?
anonymous
  • anonymous
i got 7=1 for posititive quardatic
freckles
  • freckles
I have no clue how you can conclude 7 is 1...
freckles
  • freckles
7 is greater than 1 so it cannot be 1
freckles
  • freckles
\[au^2+bu+c=0 \\ u=\frac{-b \pm \sqrt{b^2-4ac}}{2a}\]
freckles
  • freckles
all you do is enter in the a,b,c into the above formula
anonymous
  • anonymous
yes i know the rhyme for the quad. o got 1 for positive
anonymous
  • anonymous
i got 1=1
freckles
  • freckles
what did you get for u ?
anonymous
  • anonymous
i got u equals 1 for both eqautions
freckles
  • freckles
\[u=\frac{-b \pm \sqrt{b^2-4ac}}{2a} \\ \text{ we have } a=7,b=-14,c=7 \\ u=\frac{-(-14) \pm \sqrt{(-14)^2-4(7)(7)}}{2(7)} \\ u=\frac{14 \pm \sqrt{196-196}}{14} \\ u=1\]oh so you mean u=1 not 1=1..which doesn't really help us
freckles
  • freckles
ok well remember u was in the place of sin(x)
freckles
  • freckles
sin(x)=1 when x=?
anonymous
  • anonymous
1?
freckles
  • freckles
sin(1) is not 1
freckles
  • freckles
look at the unit circle if you have to for what angles on the unit circle do you have the y-coordinate is 1 on the unit circle
anonymous
  • anonymous
90 deg
freckles
  • freckles
yep so 90 deg+360 deg*k where k is a integer
freckles
  • freckles
or you prefer.... pi/2+2pi*k where k is an integer
anonymous
  • anonymous
is that the answer ?
freckles
  • freckles
yep one of those are the answer it depends on the preference of your teacher
anonymous
  • anonymous
wow thats was alot easier than i expected. when can you not use the quadratic form?
freckles
  • freckles
when it can't be written in the form au^2+bu+c=0
freckles
  • freckles
if it can be written in the form au^2+bu+c=0 then it is in quadratic form in terms of u whether u be sin(x) or cos(x) or tan(x)...
anonymous
  • anonymous
ok thank you so much

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