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If cos(theta) = -2/sqrt5, and theta is in quadrant II, find the exact value of tan(theta+ pi/4)

 Nov 25, 2018
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cos (theta)  = -2 / √5

sin theta =  1/√5

 

tan (theta + pi/4)   =

 

sin (theta + pi/4)

_______________  =

cos (theta + pi /4)

 

sin theta * cos pi/4   + cos theta * sin pi/4

_________________________________ =         

costheta * cos pi/4 -  sin theta * sin pi/4

 

 { sin pi/4 = cos pi/4 =  1 /√2 }

 

 

1/√2  [ sin theta + cos theta ]

_______________________  =

1 / √2 [ cos theta - sin theta ]

 

 

[ 1/√5  + (-2)/√5 ]

_______________   =

[ (-2)/√5  - 1/√5 ]  

 

 

[ 1 - 2 ]                  -1                 1 

________    =      ____     =    ___

[ -2 - 1 ]                  -3                3

 

 

 

cool cool cool

 Nov 25, 2018

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