anonymous
  • anonymous
can i please get help with this, i dont know how to solve it Find all solutions to the equation. 7 sin2x - 14 sin x + 2 = -5
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
there is a formula for sin(2x)
anonymous
  • anonymous
do you know what it is?
anonymous
  • anonymous
i dont think so

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anonymous
  • anonymous
sin(2x) = 2sin(x)cos(x)
anonymous
  • anonymous
Equation: 7 sin2x - 14 sin x + 2 = -5 move 2 to the other side to get?
mathmale
  • mathmale
@q12157: Very nice start, very helpful. Be certain to let mabitrix find his or her own answer(s), with your guidance.
anonymous
  • anonymous
7 sin2x -14 sinx = -3
anonymous
  • anonymous
now plug in the formula for sin(2x) to get?
anonymous
  • anonymous
also its not -3 its -7
anonymous
  • anonymous
since you are subtracting 2 on both sides
anonymous
  • anonymous
7 2sin(x)cos(x) -14 sinx = -7 ?
anonymous
  • anonymous
7 2sin(x)cos(x) is the same as 14sin(x)cos(x) right?
anonymous
  • anonymous
yes
anonymous
  • anonymous
aren't i supposed to make the equation =0?
anonymous
  • anonymous
question... is it sin(2x) or is it sin^2(x) for the problem...
anonymous
  • anonymous
if its sin^2(x)...its a totally different process lol
anonymous
  • anonymous
oh it's sin^2(x)
anonymous
  • anonymous
lol... 7 sin^2(x) - 14 sin x + 2 = -5 move -5 to other side to get: 7 sin^2(x) - 14 sin x + 7 = 0 Divide everything by 7 to get sin^2(x) - 2sin x + 1 = 0 Correct?
anonymous
  • anonymous
yea i get it better now
anonymous
  • anonymous
The trick here is now to take a variable such as B and set that equal to sin(x) so B=sin(x) Thus the equation becomes B^2-2B+1=0
anonymous
  • anonymous
Do you know how to factor this?
anonymous
  • anonymous
The equation becomes: (B-1)*(B-1)=0
anonymous
  • anonymous
Have you learnt multiplicity yet?
anonymous
  • anonymous
so so i do (sinx - 1)(sinx -1)=0 ?
anonymous
  • anonymous
Yep
anonymous
  • anonymous
so what does sin(x)=?
anonymous
  • anonymous
but why is it -1 in the parenthesis?
anonymous
  • anonymous
sinx = 1
anonymous
  • anonymous
its (sin(x) - 1)(sin(x) -1)=0
anonymous
  • anonymous
and yep
anonymous
  • anonymous
since sinx=1 what does x=?
anonymous
  • anonymous
do i do sin^-1 (1)? and thats equal pi/2?
anonymous
  • anonymous
yep! except theres a catch...
anonymous
  • anonymous
The question asks to find "all solutions"
anonymous
  • anonymous
thus (pi/2)+2pi is also a solution, cause if you go all the way around the circle it still causes sin(x) to equal 1. Thus the real answer is: (pi/2)+2pi*k where k is any positive or negative integer constant
anonymous
  • anonymous
(yes you'd have to write that full answer down on your hw to receive full credit)
anonymous
  • anonymous
oh i understand, thank you for your help!

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