Precalculus Examples

$\sin (\frac{π}{6} + 49000 π)$

Step 1

To write $49000 π$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\sin (\frac{π}{6} + 49000 π \cdot \frac{6}{6})$

Step 2

Combine fractions.

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Step 2.1

Combine $49000 π$ and $\frac{6}{6}$ .

$\sin (\frac{π}{6} + \frac{49000 π \cdot 6}{6})$

Step 2.2

Combine the numerators over the common denominator.

$\sin (\frac{π + 49000 π \cdot 6}{6})$

Step 3

Simplify the numerator.

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Step 3.1

Multiply $6$ by $49000$ .

$\sin (\frac{π + 294000 π}{6})$

Step 3.2

Add $π$ and $294000 π$ .

$\sin (\frac{294001 π}{6})$

Step 4

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

$\sin (\frac{π}{6})$

Step 5

The exact value of $\sin (\frac{π}{6})$ is $\frac{1}{2}$ .

$\frac{1}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2}$

Decimal Form:

$0.5$