anonymous
  • anonymous
PreCal Help Please
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
Solve\[4\sin^2x+4\sqrt{2} cosx-6=0\]
amoodarya
  • amoodarya
the question is not here ! or i do not see it
anonymous
  • anonymous
I just posted it before you wrote your comment

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hba
  • hba
@amoodarya Refresh your page
cgreenwade2000
  • cgreenwade2000
Substitute in for the value of sin^2(x) You know what it is?
anonymous
  • anonymous
Substitute it where? I am still confused.
cgreenwade2000
  • cgreenwade2000
sin^2(x) can be put in terms of cos^2(x)
cgreenwade2000
  • cgreenwade2000
sin^2(x) = 1-cos^2 (x) Another really important one to remember. (I hope you're writing these important ones down, especially if you plan on going further in calculus)
hartnn
  • hartnn
then put cos x =y and you get a Quadratic in 'y', which can be solved easily.
hba
  • hba
^ this sounds better
cgreenwade2000
  • cgreenwade2000
I wasn't going to suggest that.......but it makes it a lot easier. Go that route.
cgreenwade2000
  • cgreenwade2000
Don't forget to distribute when you substitute for sin^2(x)
anonymous
  • anonymous
wait so is the new equation\[4( \frac{ 1 }{\cos^2x }) + 4 \sqrt{2}cosx-6=0\]
cgreenwade2000
  • cgreenwade2000
4(1-cos^2x).......
hartnn
  • hartnn
actually, \[\huge \color{red}{\sin^2x+\cos^2x=1 \\ \implies \sin^2x =1-\cos^2x}\]
amoodarya
  • amoodarya
no |dw:1358282546908:dw|
hartnn
  • hartnn
\[\huge \color{red}{\sin^2x+\cos^2x=1 \\ \implies \sin^2x =1-\cos^2x \\ \implies 4\sin^2x=4-4\cos^2x}\]
amoodarya
  • amoodarya
|dw:1358282634437:dw|
amoodarya
  • amoodarya
simplify that
anonymous
  • anonymous
Can you rewrite that? It is hard to read
hartnn
  • hartnn
\[4\sin^2x+4\sqrt{2} cosx-6=0 \\ 4-4\cos^2x+4\sqrt{2} cosx-6=0\\4\cos^2x-4\sqrt{2} cosx+2=0 \\put \cos x=y \\ \implies 4y^2-4\sqrt2y+2=0\] can you solve this quadratic ?
cgreenwade2000
  • cgreenwade2000
That should be a -2 @hartnn
hartnn
  • hartnn
u sure ?
anonymous
  • anonymous
ok so the answer is \[\frac{ \pi }{4 }+2\pi k, \frac{ 7\pi }{4 }+2\pi k\]
hartnn
  • hartnn
how did u get that ? what values of y u got ?
amoodarya
  • amoodarya
|dw:1358282921662:dw|
cgreenwade2000
  • cgreenwade2000
@hartnn 4-6=-2
hartnn
  • hartnn
@Rosy95 did you actually solve it ?
amoodarya
  • amoodarya
|dw:1358283161601:dw|
anonymous
  • anonymous
Im' sorry, I forgot to include the rest of the question...it is solve (that long equation) for all real values of x.
hartnn
  • hartnn
@Rosy95 what answer you wrote is correct. did you solve it by yourself ? and any doubts anywhere ?
anonymous
  • anonymous
I solved it by myself but i looked at the answer choices when I got half of it.
anonymous
  • anonymous
Thanks everyone!
hartnn
  • hartnn
ok, welcome ^_^

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