+0  
 
0
1518
1
avatar

cos2x+5cosx+3=0

Guest Aug 21, 2015

Best Answer 

 #1
avatar+78750 
+10

cos2x+5cosx+3=0   ....note that cos2x = 2cos^x - 1  ....so we have.......

 

2cos^x - 1 + 5 cosx + 3  = 0     simplify

 

2cos^x + 5cosx + 2   = 0      factor

 

(2cosx + 1) (cosx + 2)  = 0     setting each factor to 0, we have......

 

2cosx + 1 = 0                             and                           cosx + 2 = 0

 

subtract 1 from each side                                            subtract 2 from each side

 

2cosx = -1                                                                cos x = -2

 

divide both sides by 2                                                this has no solution

 

cosx = -1/2

 

And the solution to this is  x  = (2/3)pi + 2pi * n    and     x = (4/3)pi + 2pi * n ....   where n is any integer

 

Here's a graph......https://www.desmos.com/calculator/wb2x5nbzfv

 

 

CPhill  Aug 21, 2015
Sort: 

1+0 Answers

 #1
avatar+78750 
+10
Best Answer

cos2x+5cosx+3=0   ....note that cos2x = 2cos^x - 1  ....so we have.......

 

2cos^x - 1 + 5 cosx + 3  = 0     simplify

 

2cos^x + 5cosx + 2   = 0      factor

 

(2cosx + 1) (cosx + 2)  = 0     setting each factor to 0, we have......

 

2cosx + 1 = 0                             and                           cosx + 2 = 0

 

subtract 1 from each side                                            subtract 2 from each side

 

2cosx = -1                                                                cos x = -2

 

divide both sides by 2                                                this has no solution

 

cosx = -1/2

 

And the solution to this is  x  = (2/3)pi + 2pi * n    and     x = (4/3)pi + 2pi * n ....   where n is any integer

 

Here's a graph......https://www.desmos.com/calculator/wb2x5nbzfv

 

 

CPhill  Aug 21, 2015

18 Online Users

avatar
avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details