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count, \(cos\alpha \),when \(sin2\alpha =5/13\) ja \(-\frac\pi4\leq\alpha \geq\frac\pi4\)

no calculator

Guest Feb 14, 2018
edited by Guest  Feb 14, 2018
edited by Guest  Feb 14, 2018
 #1
avatar+13014 
+1

.98058      You DO know there is a calculator on this website......Yes?

ElectricPavlov  Feb 14, 2018
 #2
avatar+89781 
+2

Sin (2A)  =  5/13  ...... so  ....Cos(2A)  =  12/13

 

Using a half-angle identity

 

cos (A)  =  √  [  ( 1 + cos2A)  / 2 ]  =   √  [ ( 1  + 12/13) / 2 ]  =

 

√  [  (13 + 12) / 26 }     =   √  [ 25 / 26 ] =     5 / √26  =

 

(5/26)√26

 

 And we take the positive root since the cosine is positive on the requested interval

 

 

cool cool cool

CPhill  Feb 14, 2018

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