Calculus Examples

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

Step 1

Evaluate the limit.

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Step 1.1

Move the term $\cos (2 π)$ outside of the limit because it is constant with respect to $x$ .

$\cos (2 π) lim_{x \to π} \sin (x)$

Step 1.2

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

$\cos (2 π) \sin (lim_{x \to π} x)$

Step 2

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

$\cos (2 π) \sin (π)$

Step 3

Simplify the answer.

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Step 3.1

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

$\cos (0) \sin (π)$

Step 3.2

The exact value of $\cos (0)$ is $1$ .

$1 \sin (π)$

Step 3.3

Multiply $\sin (π)$ by $1$ .

$\sin (π)$

Step 3.4

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

$\sin (0)$

Step 3.5

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

$0$