SOLUTION: find {{{cos(beta)}}} and {{{tan(beta)}}} if {{{cos(2beta)=2/3}}}, {{{3pi/2 < 2beta<2pi}}}

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Question 1134855: find cos%28beta%29 and tan%28beta%29
if cos%282beta%29=2%2F3, 3pi%2F2+%3C+2beta%3C2pi
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Cos(2B) = 2/3 in Q4
B is in Q2
——————
Cos^2(B) = (1 + cos(2B))/2 = 5/6
Cos(B) = -sqrt(30)/6
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Sin^2(B) = (1 - cos(2B))/2 = 1/6
Sin(B) = sqrt(6)/6
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Tan(B) = sin/cos = -sqrt(5)