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2 cos^2 x  3 cos x + 1 = 0 for 0 is less than or equal to x is less than 2pi
 one year ago
 one year ago
2 cos^2 x  3 cos x + 1 = 0 for 0 is less than or equal to x is less than 2pi
 one year ago
 one year ago

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dpaIncBest ResponseYou've already chosen the best response.1
the first term with the cosine... is it: \(\large 2cos^2x \) or \(\large 2cos(2x) \) i'm thinking it's the first one?
 one year ago

dpaIncBest ResponseYou've already chosen the best response.1
think of it this way.. let y=cosx so your equation becomes: \(\large 2y^23y+1=0 \) can you solve this quadratic?
 one year ago

dpaIncBest ResponseYou've already chosen the best response.1
what is/are the solutions ? y = ???
 one year ago

z3529080Best ResponseYou've already chosen the best response.0
2(2cos^2(x)1)3cosx+1=0 > 4cos^2(x)3cosx1=0 > (4cosx+1)(cosx1)=0
 one year ago

z3529080Best ResponseYou've already chosen the best response.0
so set 4cosx+1=0 or cos1 =0
 one year ago

dpaIncBest ResponseYou've already chosen the best response.1
hmmm.. i got the same but POSITIVE values... i'm double checking...
 one year ago

dpaIncBest ResponseYou've already chosen the best response.1
yeah... they should be positive: \(\large 2y^23y+1=0 \) \(\large (2y1)(y1)=0 \) so 2y  1= 0 gives y=1/2 y1 = 0 gives y=1
 one year ago

z3529080Best ResponseYou've already chosen the best response.0
oh i thought it is cos2x
 one year ago

dpaIncBest ResponseYou've already chosen the best response.1
since y=cosx, we have these two equations: \( \large cosx=\frac{1}{2}\) and \(\large cosx=1 \) can you solve these?
 one year ago

dpaIncBest ResponseYou've already chosen the best response.1
oops... that second one should be POSITIVE one...
 one year ago

dpaIncBest ResponseYou've already chosen the best response.1
do you use the unit circle?
 one year ago

joshiBest ResponseYou've already chosen the best response.0
this is probably a stupid question, but i'm a bit confused. you said let y = cosx so what happens to the first term 2cos2x? like what about the 2 infront of the x?
 one year ago

onegirlBest ResponseYou've already chosen the best response.0
@joshi its 2 cos^2 x 3 i made a mistake in typing it
 one year ago

dpaIncBest ResponseYou've already chosen the best response.1
ok... so look at what angle gives you a cosine of 1/2.... HINT: there are two of 'em from 0 to 2pi
 one year ago

joshiBest ResponseYou've already chosen the best response.0
ohhh ok that makes more sense haha
 one year ago

dpaIncBest ResponseYou've already chosen the best response.1
yeah... i got a clarification from the asker with my first question... :)
 one year ago

dpaIncBest ResponseYou've already chosen the best response.1
dw:1350069794735:dw yep... 60 degrees is one of 'em....
 one year ago

dpaIncBest ResponseYou've already chosen the best response.1
you got the second angle?
 one year ago

dpaIncBest ResponseYou've already chosen the best response.1
nope... we're still solving cosx = 1/2 , right? x=60 degrees or pi/3 is one... the second solution is in the fourth quadrant...
 one year ago

dpaIncBest ResponseYou've already chosen the best response.1
or take a look at page 3: http://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf
 one year ago

dpaIncBest ResponseYou've already chosen the best response.1
240 degrees is in the third quadrant... this is the fourth quadrant: dw:1350070347242:dw
 one year ago

dpaIncBest ResponseYou've already chosen the best response.1
yes... :) cos(60 degrees) = 1/2 and cos(300 degrees) = 1/2 now solve the other equation: cos x = 1
 one year ago

dpaIncBest ResponseYou've already chosen the best response.1
and remember, \(\large 0\color {red}{\le} x<2\pi \)
 one year ago

dpaIncBest ResponseYou've already chosen the best response.1
there should be only one solution for this one....
 one year ago

dpaIncBest ResponseYou've already chosen the best response.1
using the unit circle, what angle gives you an xcoordinate of 1?
 one year ago

dpaIncBest ResponseYou've already chosen the best response.1
yes but 2pi is not included in the interval you're looking at.. 360 degrees = 2pi so what other angle gives you an xcoordinate of 1?
 one year ago

onegirlBest ResponseYou've already chosen the best response.0
ohhh yea it will 180 degrees
 one year ago

dpaIncBest ResponseYou've already chosen the best response.1
no.. cos(180 degrees) = 1 try again....
 one year ago

dpaIncBest ResponseYou've already chosen the best response.1
cos x = 1 where \( \large 0\color {red}{\le} x<2\pi\)
 one year ago

dpaIncBest ResponseYou've already chosen the best response.1
what about the left side of \(\large 0\color {red}{\le} x<2\pi \) ???? x = 0 ? cos 0 = ???
 one year ago

dpaIncBest ResponseYou've already chosen the best response.1
ok... let's put it this way... what's an angle that is coterminal with 360 degrees?
 one year ago

onegirlBest ResponseYou've already chosen the best response.0
positive 360 and negative 360
 one year ago

dpaIncBest ResponseYou've already chosen the best response.1
no.. the angle you want is 0 because cos(0 degrees) = 1 so you have 3 solutions: x=0, 60, 300 degrees but since the problem was stated in terms of radians, i'd convert those angles.
 one year ago

onegirlBest ResponseYou've already chosen the best response.0
so it will be x=1.823 radian
 one year ago
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