anonymous
  • anonymous
Solve on interval 0,2pi
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
\[(cosx+1)(2\cos^2 x-3cosx-2)\]
anonymous
  • anonymous
ok hold on
hartnn
  • hartnn
there's no equation to solve :O what you've written is an expression, is the Q by any chance, \((cosx+1)(2\cos^2 x-3cosx-2)=0\) ?

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More answers

anonymous
  • anonymous
\[x=2\pi,x=\frac{ \pi }{ 2 },x=\frac{ \pi }{ 3 }\] \[x=\frac{ \pi }{ 6 },x=\frac{ 7\pi }{ 6 }\] \[x=\pi,x=\frac{ 2\pi }{ 3 },x=\frac{ 4\pi }{ 3 }\] \[x=2\pi,x=\frac{ \pi }{ 2 },x=\frac{ 5\pi }{ 4 }\]
anonymous
  • anonymous
no sorry thats all i have
anonymous
  • anonymous
@hartnn help?
hartnn
  • hartnn
its this only : \((cosx+1)(2\cos^2 x-3cosx-2)=0\) so, we have \((cosx+1)=0 \quad and \quad (2\cos^2 x-3cosx-2)=0\) the first one is easy, any ideas what to do for \( (2\cos^2 x-3cosx-2)=0\) ?
anonymous
  • anonymous
simplifies to \[(2cosx+1)(cosx-2)\] ?
anonymous
  • anonymous
graph it lol.
hartnn
  • hartnn
yes, \((2cosx+1)(cosx-2)=0\) is correct. now just solve these, \((2cosx+1)=0 \quad \\ (cosx-2)=0\)
anonymous
  • anonymous
how would i sole them?
hartnn
  • hartnn
2 cos x +1 =0 isolate cos x, can u ?
hartnn
  • hartnn
like for cos x -2 = 0 cos x = 2
anonymous
  • anonymous
\[cosx=-\frac{ 1 }{ 2 }\]?
hartnn
  • hartnn
thats correct, now for which values of x, is cos x = -1/2 ?
anonymous
  • anonymous
what do you mean? sorry ive been up all night!!!
hartnn
  • hartnn
i mean there are 2 angles for which cos x equals -1/2 like, 2 values for which cos x =+1/2 will be pi/3 and 5pi/3
hartnn
  • hartnn
also, cos x = 2 is not possible because cos x can take values from +1 to -1 only.
anonymous
  • anonymous
how would i find the radical?
hartnn
  • hartnn
from the unit circle, you can find that , cos x = -1/2 for x =2pi/3 and 4pi/3
anonymous
  • anonymous
okay
hartnn
  • hartnn
and cos x +1 =0 would give you cos x = -1 you know for which angle is cos x = -1 ??
anonymous
  • anonymous
do you have an example of a unit circle? i found one online but its confusing
hartnn
  • hartnn
http://en.wikipedia.org/wiki/File:Unit_circle_angles_color.svg
hartnn
  • hartnn
you just look where, x-cordinate (cos) equals, -1/2 if you search, you will find it at 2 point, x = 2pi/3 and x= 4pi/3 now search where x-co-ordinate is -1 ?
anonymous
  • anonymous
\[\pi,\frac{ 3\pi }{ 2 }?\]
hartnn
  • hartnn
not at 3pi/2 at 3pi/2, x-cordinate = 0 so, only x= pi
anonymous
  • anonymous
oops sorry
hartnn
  • hartnn
that means cos pi=-1
hartnn
  • hartnn
now we have only 3 roots , x=pi, 2pi/3,4pi/3
anonymous
  • anonymous
so it would be C?
hartnn
  • hartnn
yes :) any doubts ?
anonymous
  • anonymous
Yay! you're so smart! :)
hartnn
  • hartnn
you too are smart enough :)
anonymous
  • anonymous
lol smart enough! :) gee thanks!
hartnn
  • hartnn
welcome ^_^

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