Calculus Examples

$\tan^{-1} (\frac{2 - \sqrt{8}}{2})$

Step 1

To convert radians to degrees, multiply by $\frac{180}{π}$ , since a full circle is $360 °$ or $2 π$ radians.

$(\tan^{-1} (\frac{2 - \sqrt{8}}{2})) \cdot \frac{180 °}{π}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $8$ as $2^{2} \cdot 2$ .

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Step 2.1.1

Factor $4$ out of $8$ .

$\tan^{-1} (\frac{2 - \sqrt{4 (2)}}{2}) \cdot \frac{180}{π}$

Step 2.1.2

Rewrite $4$ as $2^{2}$ .

$\tan^{-1} (\frac{2 - \sqrt{2^{2} \cdot 2}}{2}) \cdot \frac{180}{π}$

Step 2.2

Pull terms out from under the radical.

$\tan^{-1} (\frac{2 - (2 \sqrt{2})}{2}) \cdot \frac{180}{π}$

Step 2.3

Multiply $2$ by $- 1$ .

$\tan^{-1} (\frac{2 - 2 \sqrt{2}}{2}) \cdot \frac{180}{π}$

Step 3

Cancel the common factor of $2 - 2 \sqrt{2}$ and $2$ .

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Step 3.1

Factor $2$ out of $2$ .

$\tan^{-1} (\frac{2 \cdot 1 - 2 \sqrt{2}}{2}) \cdot \frac{180}{π}$

Step 3.2

Factor $2$ out of $- 2 \sqrt{2}$ .

$\tan^{-1} (\frac{2 \cdot 1 + 2 (- \sqrt{2})}{2}) \cdot \frac{180}{π}$

Step 3.3

Factor $2$ out of $2 (1) + 2 (- \sqrt{2})$ .

$\tan^{-1} (\frac{2 (1 - \sqrt{2})}{2}) \cdot \frac{180}{π}$

Step 3.4

Cancel the common factors.

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Step 3.4.1

Factor $2$ out of $2$ .

$\tan^{-1} (\frac{2 (1 - \sqrt{2})}{2 (1)}) \cdot \frac{180}{π}$

Step 3.4.2

Cancel the common factor.

$\tan^{-1} (\frac{2 (1 - \sqrt{2})}{2 \cdot 1}) \cdot \frac{180}{π}$

Step 3.4.3

Rewrite the expression.

$\tan^{-1} (\frac{1 - \sqrt{2}}{1}) \cdot \frac{180}{π}$

Step 3.4.4

Divide $1 - \sqrt{2}$ by $1$ .

$\tan^{-1} (1 - \sqrt{2}) \cdot \frac{180}{π}$

Step 4

Evaluate $\tan^{-1} (1 - \sqrt{2})$ .

$- \frac{π}{8} \cdot \frac{180}{π}$

Step 5

Cancel the common factor of $π$ .

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Step 5.1

Move the leading negative in $- \frac{π}{8}$ into the numerator.

$\frac{- π}{8} \cdot \frac{180}{π}$

Step 5.2

Factor $π$ out of $- π$ .

$\frac{π \cdot - 1}{8} \cdot \frac{180}{π}$

Step 5.3

Cancel the common factor.

$\frac{π \cdot - 1}{8} \cdot \frac{180}{π}$

Step 5.4

Rewrite the expression.

$\frac{- 1}{8} \cdot 180$

Step 6

Cancel the common factor of $4$ .

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Step 6.1

Factor $4$ out of $8$ .

$\frac{- 1}{4 (2)} \cdot 180$

Step 6.2

Factor $4$ out of $180$ .

$\frac{- 1}{4 \cdot 2} \cdot (4 \cdot 45)$

Step 6.3

Cancel the common factor.

$\frac{- 1}{4 \cdot 2} \cdot (4 \cdot 45)$

Step 6.4

Rewrite the expression.

$\frac{- 1}{2} \cdot 45$

Step 7

Combine $\frac{- 1}{2}$ and $45$ .

$\frac{- 1 \cdot 45}{2}$

Step 8

Simplify the expression.

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Step 8.1

Multiply $- 1$ by $45$ .

$\frac{- 45}{2}$

Step 8.2

Move the negative in front of the fraction.

$- \frac{45}{2}$

Step 9

Convert to a decimal.

$- 22.5 °$