What is the limit as θ approaches 0 of (sin(5θ))/(sin(2θ)) ?

The limit as θ approaches 0 of (sin(5θ))/(sin(2θ)) is 5/2

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limit as θ approaches 0 of (sin(5θ))/(sin(2θ))

θ \to 0 lim (\frac{sin ( 5 θ )}{sin ( 2 θ )})

\frac{5}{2}

Decimal Notation

2.5

Solution steps

θ \to 0 lim (\frac{sin ( 5 θ )}{sin ( 2 θ )})

Apply L'Hopital's Rule

: θ \to 0 lim (\frac{cos ( 5 θ ) \cdot 5}{cos ( 2 θ ) \cdot 2})

= θ \to 0 lim (\frac{cos ( 5 θ ) \cdot 5}{cos ( 2 θ ) \cdot 2})

Plug in the value

θ = 0

= \frac{cos ( 5 \cdot 0 ) \cdot 5}{cos ( 2 \cdot 0 ) \cdot 2}

Simplify

\frac{cos ( 5 \cdot 0 ) \cdot 5}{cos ( 2 \cdot 0 ) \cdot 2} : \frac{5}{2}

= \frac{5}{2}

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What is the limit as θ approaches 0 of (sin(5θ))/(sin(2θ)) ?
The limit as θ approaches 0 of (sin(5θ))/(sin(2θ)) is 5/2