Finite Math Examples

$\sin (2 π) - \frac{π}{6} + \cos (\frac{π}{2}) - \frac{π}{3}$

Step 1

Simplify each term.

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Step 1.1

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

$\sin (0) - \frac{π}{6} + \cos (\frac{π}{2}) - \frac{π}{3}$

Step 1.2

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

$0 - \frac{π}{6} + \cos (\frac{π}{2}) - \frac{π}{3}$

Step 1.3

The exact value of $\cos (\frac{π}{2})$ is $0$ .

$0 - \frac{π}{6} + 0 - \frac{π}{3}$

Step 2

Simplify by adding zeros.

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Step 2.1

Subtract $\frac{π}{6}$ from $0$ .

$- \frac{π}{6} + 0 - \frac{π}{3}$

Step 2.2

Add $- \frac{π}{6}$ and $0$ .

$- \frac{π}{6} - \frac{π}{3}$

Step 3

To write $- \frac{π}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{π}{6} - \frac{π}{3} \cdot \frac{2}{2}$

Step 4

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{π}{3}$ by $\frac{2}{2}$ .

$- \frac{π}{6} - \frac{π \cdot 2}{3 \cdot 2}$

Step 4.2

Multiply $3$ by $2$ .

$- \frac{π}{6} - \frac{π \cdot 2}{6}$

Step 5

Combine the numerators over the common denominator.

$\frac{- π - π \cdot 2}{6}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $2$ by $- 1$ .

$\frac{- π - 2 π}{6}$

Step 6.2

Subtract $2 π$ from $- π$ .

$\frac{- 3 π}{6}$

Step 7

Reduce the expression by cancelling the common factors.

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Step 7.1

Cancel the common factor of $- 3$ and $6$ .

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Step 7.1.1

Factor $3$ out of $- 3 π$ .

$\frac{3 (- π)}{6}$

Step 7.1.2

Cancel the common factors.

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Step 7.1.2.1

Factor $3$ out of $6$ .

$\frac{3 (- π)}{3 (2)}$

Step 7.1.2.2

Cancel the common factor.

$\frac{3 (- π)}{3 \cdot 2}$

Step 7.1.2.3

Rewrite the expression.

$\frac{- π}{2}$

Step 7.2

Move the negative in front of the fraction.

$- \frac{π}{2}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- \frac{π}{2}$

Decimal Form:

$- 1.57079632 \dots$