anonymous
  • anonymous
sin2x - 14 sin x + 2 = -5
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
solve for x?
anonymous
  • anonymous
solve for sin x
anonymous
  • anonymous
is the first term \[\sin^2x\]

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anonymous
  • anonymous
yes sorry my bad
anonymous
  • anonymous
i call this a batman quadratic. 'a quadratic in disguise'
Jhannybean
  • Jhannybean
\[\large \sin^2 (x) -14 \sin x +2 =-5 \] think about \[\large ax^2 +bx+ c= 0\] and solve it like a quadratic.
anonymous
  • anonymous
Find all solutions to the equation. would it be sin x=1?
Jhannybean
  • Jhannybean
lol chris.
anonymous
  • anonymous
thats wat mi teacher used to say
Jhannybean
  • Jhannybean
Or maaybe you can solve it by completing the square?
anonymous
  • anonymous
ohhh snhnap i forgot to add the 7
anonymous
  • anonymous
7 sin^2x - 14 sin x + 2 = -5
Jhannybean
  • Jhannybean
?...
anonymous
  • anonymous
sorry -.-
Jhannybean
  • Jhannybean
\[\large \ 7\sin^2 (x) -14 \sin x +2 =-5\]
anonymous
  • anonymous
that would make sense. thats easier.
anonymous
  • anonymous
add 5 to both sides then divide 7 to both sides.
anonymous
  • anonymous
sin^2(x)-2sinx+1 sinx(sinx-1)?
anonymous
  • anonymous
i feel like jhannybean is going to solve this nicely.
Jhannybean
  • Jhannybean
Yeah...we can solve it utilizing the quadratic equation. first,move the -5 to the other side. \[\large \ \frac{7\sin^2 (x)}{7} -\frac{14 \sin( x)}{7} +\frac{7}{7} =0\]\[\large \sin^2(x) -2\sin(x)+1=0\] quadratic formula. \[\large x= \frac{-(-2) \pm \sqrt{(-2)^2 -4(1)(1)}}{2}\]\[\large x= \frac{2}{2} = 1\]
Jhannybean
  • Jhannybean
Oh did i forget something...
anonymous
  • anonymous
sinx=1?
Jhannybean
  • Jhannybean
How would you solve this, chris?
anonymous
  • anonymous
kk.
Jhannybean
  • Jhannybean
Yes i believe im solving it the right way, lol.
anonymous
  • anonymous
we already know |dw:1371530910398:dw| where X=sinx
Jhannybean
  • Jhannybean
Ahh... true enough.
Jhannybean
  • Jhannybean
x=1, yes?
anonymous
  • anonymous
|dw:1371530981106:dw|
anonymous
  • anonymous
|dw:1371531037732:dw|
Jhannybean
  • Jhannybean
\[\large \sin(x) = 1\]\[\large \sin^{-1}(1) = x\] and i don't know how to write the general format...:| how do you know it's 2kpi...
Jhannybean
  • Jhannybean
Ohh..are sin and cos BOTH 2kpi?..
anonymous
  • anonymous
unit circle|dw:1371531182625:dw|
anonymous
  • anonymous
pi/2 occurs every 2k*pi
Jhannybean
  • Jhannybean
Ohh YOU HAVE TO SEE WHEN IT OCCURS!!!
Jhannybean
  • Jhannybean
ok i remember now.
anonymous
  • anonymous
haha!
Jhannybean
  • Jhannybean
Good job. :)
anonymous
  • anonymous
cant believe its still in mi brain
Jhannybean
  • Jhannybean
lol. do you know how we solved it @Megafox
anonymous
  • anonymous
gd idea.
Jhannybean
  • Jhannybean
not we, he*
anonymous
  • anonymous
team effort
Jhannybean
  • Jhannybean
:) ty
anonymous
  • anonymous
So in regards to "Find all solutions to the equation." what would the solutions be?
anonymous
  • anonymous
|dw:1371531482626:dw|
anonymous
  • anonymous
if there is strictly no domain
anonymous
  • anonymous
x= pi/2, +pi?
anonymous
  • anonymous
+kpi
anonymous
  • anonymous
wha does the k represent?
anonymous
  • anonymous
any positive or negative integer
anonymous
  • anonymous
|dw:1371531591766:dw|
anonymous
  • anonymous
^ Wait what?
anonymous
  • anonymous
i have no idea. just stick with our method ok. i graphed it and mi answer if perfectly correct.

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