What is the limit as θ approaches 0 of (1-cos(θ))/θ ?

The limit as θ approaches 0 of (1-cos(θ))/θ is 0

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limit as θ approaches 0 of (1-cos(θ))/θ

θ \to 0 lim (\frac{1 - cos ( θ )}{θ})

0

Solution steps

θ \to 0 lim (\frac{1 - cos ( θ )}{θ})

Apply L'Hopital's Rule

= θ \to 0 lim (\frac{sin ( θ )}{1})

Plug in the value

θ = 0

= \frac{sin ( 0 )}{1}

Simplify

\frac{sin ( 0 )}{1} : 0

= 0

What is the limit as θ approaches 0 of (1-cos(θ))/θ ?
The limit as θ approaches 0 of (1-cos(θ))/θ is 0