Trigonometry Examples

$h = 2 π r^{2} + π r T$

Step 1

Rewrite the equation as $2 π r^{2} + π r T = h$ .

$2 π r^{2} + π r T = h$

Step 2

Subtract $2 π r^{2}$ from both sides of the equation.

$π r T = h - 2 π r^{2}$

Step 3

Divide each term in $π r T = h - 2 π r^{2}$ by $π r$ and simplify.

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Step 3.1

Divide each term in $π r T = h - 2 π r^{2}$ by $π r$ .

$\frac{π r T}{π r} = \frac{h}{π r} + \frac{- 2 π r^{2}}{π r}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $π$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{π r T}{π r} = \frac{h}{π r} + \frac{- 2 π r^{2}}{π r}$

Step 3.2.1.2

Rewrite the expression.

$\frac{r T}{r} = \frac{h}{π r} + \frac{- 2 π r^{2}}{π r}$

Step 3.2.2

Cancel the common factor of $r$ .

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Step 3.2.2.1

Cancel the common factor.

$\frac{r T}{r} = \frac{h}{π r} + \frac{- 2 π r^{2}}{π r}$

Step 3.2.2.2

Divide $T$ by $1$ .

$T = \frac{h}{π r} + \frac{- 2 π r^{2}}{π r}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

Cancel the common factor of $π$ .

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Step 3.3.1.1.1

Cancel the common factor.

$T = \frac{h}{π r} + \frac{- 2 π r^{2}}{π r}$

Step 3.3.1.1.2

Rewrite the expression.

$T = \frac{h}{π r} + \frac{- 2 r^{2}}{r}$

Step 3.3.1.2

Cancel the common factor of $r^{2}$ and $r$ .

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Step 3.3.1.2.1

Factor $r$ out of $- 2 r^{2}$ .

$T = \frac{h}{π r} + \frac{r (- 2 r)}{r}$

Step 3.3.1.2.2

Cancel the common factors.

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Step 3.3.1.2.2.1

Raise $r$ to the power of $1$ .

$T = \frac{h}{π r} + \frac{r (- 2 r)}{r^{1}}$

Step 3.3.1.2.2.2

Factor $r$ out of $r^{1}$ .

$T = \frac{h}{π r} + \frac{r (- 2 r)}{r \cdot 1}$

Step 3.3.1.2.2.3

Cancel the common factor.

$T = \frac{h}{π r} + \frac{r (- 2 r)}{r \cdot 1}$

Step 3.3.1.2.2.4

Rewrite the expression.

$T = \frac{h}{π r} + \frac{- 2 r}{1}$

Step 3.3.1.2.2.5

Divide $- 2 r$ by $1$ .

$T = \frac{h}{π r} - 2 r$