What is the limit as θ approaches 0 of (sin(θ))/(sin(2θ)) ?

The limit as θ approaches 0 of (sin(θ))/(sin(2θ)) is 1/2

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limit as θ approaches 0 of (sin(θ))/(sin(2θ))

θ \to 0 lim (\frac{sin ( θ )}{sin ( 2 θ )})

\frac{1}{2}

Decimal

0.5

Solution steps

θ \to 0 lim (\frac{sin ( θ )}{sin ( 2 θ )})

Apply L'Hopital's Rule

= θ \to 0 lim (\frac{cos ( θ )}{cos ( 2 θ ) \cdot 2})

Plug in the value

θ = 0

= \frac{cos ( 0 )}{cos ( 2 \cdot 0 ) \cdot 2}

Simplify

\frac{cos ( 0 )}{cos ( 2 \cdot 0 ) \cdot 2} : \frac{1}{2}

= \frac{1}{2}

What is the limit as θ approaches 0 of (sin(θ))/(sin(2θ)) ?
The limit as θ approaches 0 of (sin(θ))/(sin(2θ)) is 1/2