SOLUTION: Find the value of tan2 x on the interval (0,2pi) given cos x = (5/9)

Algebra ->  Test -> SOLUTION: Find the value of tan2 x on the interval (0,2pi) given cos x = (5/9)      Log On


   

Question 971581: Find the value of tan2 x on the interval (0,2pi) given cos x = (5/9)
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Find the value of tan2 x on the interval (0,2pi) given cos x = (5/9)
sinx=√(1-cos^2(x))=√(1-25/81)=√(56/81)=√56/9
sin(2x)=2sinxcosx=2√56/9*5/9=10√56/81
cos(2x)=cos^2(x)-sin^2(x)=25/81-56/81=-31/81
tan(2x)=sin(2x)/cos(2x)=-(10√56)/31