anonymous
  • anonymous
solve 8cos^2(x)-6cos(x)+1=0
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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Nnesha
  • Nnesha
that's the quadratic equation let cos(x) = y to make it simple \[\huge\rm 8y^2-6y+1=0\] now can you factor the quadratic equation ?
Nnesha
  • Nnesha
A)yes B) no C) maybe pick one
anonymous
  • anonymous
yes

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Nnesha
  • Nnesha
okay :=)) good try to factor and then post your work
anonymous
  • anonymous
8y^2 -6y +1 = (2y-1)(4y-1) ---> 2y*4y=8y^2, 2y*-1=-2y, -1*4y= -4y, -1*-1=1 therefore 8y^2 -2y -4y +1= 8y^2 -6y +1 so it is factorable and above is it's factored form
Nnesha
  • Nnesha
that's correct! nice job \[\rm \color{ReD}{(2y-1)}\color{blue}{(4y-1)}=0\] set them equal to zero \[\rm \color{reD}{2y-1}=0\] and \[\rm \color{blue}{4y-1}=0\] solve for y
Nnesha
  • Nnesha
btw we should multiply the same two numbers to get the product of AC (a=leading coefficient c=constant term)so instead multiplying separately 2y and 4y by -1 you can just do -2y * -4y = 8y^2 \[\rm negative*negative =positive \]
anonymous
  • anonymous
alright I will keep that in mind thank you
Nnesha
  • Nnesha
bec \[\rm -2y*-4y=8y^2\] \[\rm -2y-6y=-6y\] \[2y+4y\cancel{= } -6y\]
Nnesha
  • Nnesha
but that's the same thing after we multiply them by negative one alright so what do you get for y ? :=))
anonymous
  • anonymous
y= 1/2 , 1/4
Nnesha
  • Nnesha
that's correct now we can replace y with cos(x) so cos(x) =1/2 , cos(x)=1/4 to find an angle we should take invs cos here is an example \[\large\rm \sin(x) = a \rightarrow x=\sin^{-1}(a)\] invssin is same as arcsin invscos is same as arccos
Nnesha
  • Nnesha
^^in that example x is an angle
anonymous
  • anonymous
so arccos(1/2) = X1, and arccos(1/4) = X2.
Nnesha
  • Nnesha
yes that's correct you can use unit circle for 1/2 but i guess you have to use calculator for 1/4 i hope you know on the unit circle x-coordinate = cos and y-coordinate = sin
anonymous
  • anonymous
alirght so x = 1/3pi and x = 1.318...
Nnesha
  • Nnesha
oh do you need in radian or degree ? if you need radian then keep it in fraction form
Nnesha
  • Nnesha
|dw:1447594729424:dw| there is another angle where cos =1/2
anonymous
  • anonymous
don't worry it is all good, huge help btw thank you!
Nnesha
  • Nnesha
np :=))

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