You can put this solution on YOUR website! Find the exact value of the given expression.
tan(1/2 cos^-1(2/3))
let x=angle whose cos=2/3
cosx=2/3
sinx=√(1-cos^2x)=√(1-4/9)=√(5/9)=√5/3
tan(1/2 cos^-1(2/3))=tan(x/2)
Identity: tan(x/2)=sinx/(1+cosx)=(√5/3)/(1+(2/3))=(√5/3)/(5/3)=√5/5
calculator check:
cosx=2/3
x≈48.19˚
x/2≈24.09
tan(x/2)≈tan(24.09)≈0.4471…
exact value as calculated=√5/5≈0.4471…
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