Calculus Examples

$\frac{lim_{x \to π} \sin (x)}{1 - \cos (x)}$

Step 1

Move the limit inside the trig function because sine is continuous.

$\frac{\sin (lim_{x \to π} x)}{1 - \cos (x)}$

Step 2

Evaluate the limit of $x$ by plugging in $π$ for $x$ .

$\frac{\sin (π)}{1 - \cos (x)}$

Step 3

Simplify the answer.

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Step 3.1

Simplify the numerator.

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Step 3.1.1

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

$\frac{\sin (0)}{1 - \cos (x)}$

Step 3.1.2

The exact value of $\sin (0)$ is $0$ .

$\frac{0}{1 - \cos (x)}$

Step 3.2

Divide $0$ by $1 - \cos (x)$ .

$0$