Trigonometry Examples

$900 π = 4 π r^{2}$

Step 1

Rewrite the equation as $4 π r^{2} = 900 π$ .

$4 π r^{2} = 900 π$

Step 2

Divide each term in $4 π r^{2} = 900 π$ by $4 π$ and simplify.

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Step 2.1

Divide each term in $4 π r^{2} = 900 π$ by $4 π$ .

$\frac{4 π r^{2}}{4 π} = \frac{900 π}{4 π}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $4$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{4 π r^{2}}{4 π} = \frac{900 π}{4 π}$

Step 2.2.1.2

Rewrite the expression.

$\frac{π r^{2}}{π} = \frac{900 π}{4 π}$

Step 2.2.2

Cancel the common factor of $π$ .

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Step 2.2.2.1

Cancel the common factor.

$\frac{π r^{2}}{π} = \frac{900 π}{4 π}$

Step 2.2.2.2

Divide $r^{2}$ by $1$ .

$r^{2} = \frac{900 π}{4 π}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Cancel the common factor of $900$ and $4$ .

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Step 2.3.1.1

Factor $4$ out of $900 π$ .

$r^{2} = \frac{4 (225 π)}{4 π}$

Step 2.3.1.2

Cancel the common factors.

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Step 2.3.1.2.1

Factor $4$ out of $4 π$ .

$r^{2} = \frac{4 (225 π)}{4 (π)}$

Step 2.3.1.2.2

Cancel the common factor.

$r^{2} = \frac{4 (225 π)}{4 π}$

Step 2.3.1.2.3

Rewrite the expression.

$r^{2} = \frac{225 π}{π}$

Step 2.3.2

Cancel the common factor of $π$ .

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Step 2.3.2.1

Cancel the common factor.

$r^{2} = \frac{225 π}{π}$

Step 2.3.2.2

Divide $225$ by $1$ .

$r^{2} = 225$

Step 3

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$r = \pm \sqrt{225}$

Step 4

Simplify $\pm \sqrt{225}$ .

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Step 4.1

Rewrite $225$ as $15^{2}$ .

$r = \pm \sqrt{15^{2}}$

Step 4.2

Pull terms out from under the radical, assuming positive real numbers.

$r = \pm 15$

Step 5

The complete solution is the result of both the positive and negative portions of the solution.

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Step 5.1

First, use the positive value of the $\pm$ to find the first solution.

$r = 15$

Step 5.2

Next, use the negative value of the $\pm$ to find the second solution.

$r = - 15$

Step 5.3

The complete solution is the result of both the positive and negative portions of the solution.

$r = 15, - 15$