Calculus Examples

$lim_{x \to 2 π} \frac{\sin (x)}{\cos (x)}$

Step 1

Convert from $\frac{\sin (x)}{\cos (x)}$ to $\tan (x)$ .

$lim_{x \to 2 π} \tan (x)$

Step 2

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

$\tan (lim_{x \to 2 π} x)$

Step 3

Evaluate the limit of $x$ by plugging in $2 π$ for $x$ .

$\tan (2 π)$

Step 4

Simplify the answer.

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Step 4.1

Subtract full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$\tan (0)$

Step 4.2

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

$0$