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If \(\sin x + \cos x = \frac{1}{5}\) and \(0 < x < \pi,\) find \(\tan x.\)

 Nov 15, 2019
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sin x +  cos x  =   1/5         squrare both sides

 

sin^2x +  2sinxcosx   + cos^2x  =  1/25

 

(sin^2x +cos^2x  )  + 2sin x cos x   =1/25

 

1   +  sin (2x)  =  1/25

 

sin (2x )  =   1/25  - 1

 

sin (2x)  =   -24/25

 

Let  2x  =  A

 

So

 

arcsin (-24/25)   =   A   ≈  -1.288 rads  =     pi + 1.288 rads ≈  4.43 rads

 

So  

 

2x   = 4.43 rads

x  =   2.215 rads

 

So      tan (2.215)  ≈ -1.33  

 

 

cool cool cool

 Nov 15, 2019

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