Saturday, October 2, 2010

What is t if u(v(t))=1? u(v)=cosv v(t)=t^2

To find t if u(v(t))=1 , u(v)=cosv and
v(t)=t^2.


Given u(v) = cosv and v(t) =
t^2.


Therefore the composite function u(v(t)) = 
cost^2.


Therefore u(v(t)) = 1 implies cost^2 =
1.


cost^2 = 1 => t^2 = 2n*pi, where n =
0,1,2,3,.....


t = +sqrt(2n*pi),
or t = -sqrt(2n*pi), for n =
0,1,2,3...

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