Find the range of the function : f(theta) = 2 sin theta/( 2 sin theta -1 )

Answer 1

Transform: f(Θ) = 1 + 1/( 2sinΘ - 1 )

Sin function range:

-1 ≤ sinΘ ≤ 1

Multiply by 2 and add 1:

-3 ≤ 2sinΘ -1 ≤ 1

The reciprocal range:

-∞ < 1/( 2sinΘ - 1 ) ≤ -1/3 or 1 ≤ 1/( 2sinΘ - 1 ) < ∞

Finally, add 1:

-∞ < f(Θ) ≤ 2/3 or 2 ≤ f(Θ)< ∞

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