Calculus Examples

$lim_{x \to 6} \sin (\frac{π \cdot 6}{2})$

Step 1

Cancel the common factor of $6$ and $2$ .

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Step 1.1

Factor $2$ out of $π \cdot 6$ .

$lim_{x \to 6} \sin (\frac{2 (π \cdot 3)}{2})$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $2$ out of $2$ .

$lim_{x \to 6} \sin (\frac{2 (π \cdot 3)}{2 (1)})$

Step 1.2.2

Cancel the common factor.

$lim_{x \to 6} \sin (\frac{2 (π \cdot 3)}{2 \cdot 1})$

Step 1.2.3

Rewrite the expression.

$lim_{x \to 6} \sin (\frac{π \cdot 3}{1})$

Step 1.2.4

Divide $π \cdot 3$ by $1$ .

$lim_{x \to 6} \sin (π \cdot 3)$

Step 2

Evaluate the limit of $\sin (π \cdot 3)$ which is constant as $x$ approaches $6$ .

$\sin (π \cdot 3)$

Step 3

Simplify the answer.

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Step 3.1

Move $3$ to the left of $π$ .

$\sin (3 \cdot π)$

Step 3.2

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

$\sin (π)$

Step 3.3

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

$\sin (0)$

Step 3.4

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

$0$