Precalculus Examples

$(- 2.5, \frac{π}{6})$ , $(- 1.9, - \frac{π}{3})$

Step 1

Use the distance formula to determine the distance between the two points.

$Distance = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}$

Step 2

Substitute the actual values of the points into the distance formula.

$\sqrt{{((- 1.9) - (- 2.5))}^{2} + {((- \frac{π}{3}) - \frac{π}{6})}^{2}}$

Step 3

Simplify.

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Step 3.1

Multiply $- 1$ by $- 2.5$ .

$\sqrt{{(- 1.9 + 2.5)}^{2} + {((- \frac{π}{3}) - \frac{π}{6})}^{2}}$

Step 3.2

Add $- 1.9$ and $2.5$ .

$\sqrt{{0.6}^{2} + {((- \frac{π}{3}) - \frac{π}{6})}^{2}}$

Step 3.3

Raise $0.6$ to the power of $2$ .

$\sqrt{0.36 + {((- \frac{π}{3}) - \frac{π}{6})}^{2}}$

Step 3.4

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

$\sqrt{0.36 + {(- \frac{π}{3} \cdot \frac{2}{2} - \frac{π}{6})}^{2}}$

Step 3.5

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

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Step 3.5.1

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

$\sqrt{0.36 + {(- \frac{π \cdot 2}{3 \cdot 2} - \frac{π}{6})}^{2}}$

Step 3.5.2

Multiply $3$ by $2$ .

$\sqrt{0.36 + {(- \frac{π \cdot 2}{6} - \frac{π}{6})}^{2}}$

Step 3.6

Combine the numerators over the common denominator.

$\sqrt{0.36 + {(\frac{- π \cdot 2 - π}{6})}^{2}}$

Step 3.7

Simplify the numerator.

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Step 3.7.1

Multiply $2$ by $- 1$ .

$\sqrt{0.36 + {(\frac{- 2 π - π}{6})}^{2}}$

Step 3.7.2

Subtract $π$ from $- 2 π$ .

$\sqrt{0.36 + {(\frac{- 3 π}{6})}^{2}}$

Step 3.8

Reduce the expression by cancelling the common factors.

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Step 3.8.1

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

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Step 3.8.1.1

Factor $3$ out of $- 3 π$ .

$\sqrt{0.36 + {(\frac{3 (- π)}{6})}^{2}}$

Step 3.8.1.2

Cancel the common factors.

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Step 3.8.1.2.1

Factor $3$ out of $6$ .

$\sqrt{0.36 + {(\frac{3 (- π)}{3 (2)})}^{2}}$

Step 3.8.1.2.2

Cancel the common factor.

$\sqrt{0.36 + {(\frac{3 (- π)}{3 \cdot 2})}^{2}}$

Step 3.8.1.2.3

Rewrite the expression.

$\sqrt{0.36 + {(\frac{- π}{2})}^{2}}$

Step 3.8.2

Move the negative in front of the fraction.

$\sqrt{0.36 + {(- \frac{π}{2})}^{2}}$

Step 3.9

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 3.9.1

Apply the product rule to $- \frac{π}{2}$ .

$\sqrt{0.36 + {(- 1)}^{2} {(\frac{π}{2})}^{2}}$

Step 3.9.2

Apply the product rule to $\frac{π}{2}$ .

$\sqrt{0.36 + {(- 1)}^{2} \frac{π^{2}}{2^{2}}}$

Step 3.10

Simplify the expression.

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Step 3.10.1

Raise $- 1$ to the power of $2$ .

$\sqrt{0.36 + 1 \frac{π^{2}}{2^{2}}}$

Step 3.10.2

Multiply $\frac{π^{2}}{2^{2}}$ by $1$ .

$\sqrt{0.36 + \frac{π^{2}}{2^{2}}}$

Step 3.10.3

Raise $2$ to the power of $2$ .

$\sqrt{0.36 + \frac{π^{2}}{4}}$

Step 3.11

Add $0.36$ and $\frac{π^{2}}{4}$ .

$\sqrt{2.8274011}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{2.8274011}$

Decimal Form:

$1.68148776 \dots$

Step 5