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Solve 3*sin(x)^2 = 8*cos(x).

 Dec 5, 2019
 #1
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3sin^2 x  = 8 cos x

 

3 ( 1 - cos^2 x)  = 8 cos x

 

3 - 3cos^2 x  = 8 cos x      rearrange as

 

3cos^2 x + 8cos x  -  3  = 0       let   cos x  =   m

 

3m^2  + 8m  - 3   = 0

 

(3m  - 1) ( m + 3)  = 0

 

The second factor has no real solutions for the  cosine

 

So

 

3m -  1  = 0

 

3m  = 1

m  =1/3

 

So

 

cos x = 1/3    take the  arccos

 

arccos  (1/3)  =  x  ≈ 70.53°  +  2pi * n        where n is an integer

 

And

 

x=  360 - 70.53   ≈  289.47° +  2 pi * n      where n is an integer

 

 

cool cool cool

 Dec 5, 2019

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