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

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

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

θ \to 0 lim (\frac{cos ( θ ) - 1}{sin ( θ )})

0

Solution steps

θ \to 0 lim (\frac{cos ( θ ) - 1}{sin ( θ )})

Apply L'Hopital's Rule

: θ \to 0 lim (\frac{- sin ( θ )}{cos ( θ )})

= θ \to 0 lim (\frac{- sin ( θ )}{cos ( θ )})

Plug in the value

θ = 0

= \frac{- sin ( 0 )}{cos ( 0 )}

Simplify

\frac{- sin ( 0 )}{cos ( 0 )} : 0

= 0

y = x^{3} + x^{2}, y = 6 x

f (t) = 2 t^{4}

\frac{d}{d x} (\frac{e ^{x}}{5 x ^{2} + 1})

\int π sin (\frac{n x}{2}) d x

\frac{d}{d x} (6 x^{3} - 9 x + 4)

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