+0  
 
+3
208
2
avatar+7154 

This question tripped me up at first but then I figured out the correct answer. I thought it was a neat question if anyone wants to try it just for fun.  laugh

 

Given  tan θ = 20/21  and  180° < θ < 270° ,  find the exact value of  cos(θ/2) .

hectictar  Mar 21, 2018
 #1
avatar+87294 
+4

θ  ≈ 223.6  ....  so  .... θ/2    will lie in the 2nd quadrant

 

r  =  √[ 20^2 + 21^2 ]   =  √841  =  29

 

cos (θ)  =  -21/  29

 

cos (θ/2)  =   - √  [  (  1  + ( -21 / 29 ) ) / 2 ]

 

cos (θ/2)  =    -  √ [ (29 - 21) / (2*29) ]  = -  √ [ (8) / (2*29) ]   = - √ [ 4 /29) ] =

 

-   2 / √ 29

 

 

cool cool cool

CPhill  Mar 21, 2018
 #2
avatar+7154 
+3

Ah you got it!!

 

I got messed up because if you try to check it in WolframAlpha by entering

 

cos(atan(20/21)/2)

 

you get a different answer, but if you enter

 

cos((atan(20/21)+pi)/2)

 

it gives the right answer.  smiley

hectictar  Mar 21, 2018

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