Calculus Examples

$\arctan (\frac{2 + \sqrt{8}}{2})$

Step 1

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

$(\arctan (\frac{2 + \sqrt{8}}{2})) \cdot \frac{180 °}{π}$

Step 2

Simplify the numerator.

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

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Factor $4$ out of $8$ .

$\arctan (\frac{2 + \sqrt{4 (2)}}{2}) \cdot \frac{180}{π}$

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

$\arctan (\frac{2 + \sqrt{2^{2} \cdot 2}}{2}) \cdot \frac{180}{π}$

Pull terms out from under the radical.

$\arctan (\frac{2 + 2 \sqrt{2}}{2}) \cdot \frac{180}{π}$

Step 3

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

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Factor $2$ out of $2$ .

$\arctan (\frac{2 \cdot 1 + 2 \sqrt{2}}{2}) \cdot \frac{180}{π}$

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

$\arctan (\frac{2 \cdot 1 + 2 (\sqrt{2})}{2}) \cdot \frac{180}{π}$

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

$\arctan (\frac{2 (1 + \sqrt{2})}{2}) \cdot \frac{180}{π}$

Cancel the common factors.

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Factor $2$ out of $2$ .

$\arctan (\frac{2 (1 + \sqrt{2})}{2 (1)}) \cdot \frac{180}{π}$

Cancel the common factor.

$\arctan (\frac{2 (1 + \sqrt{2})}{2 \cdot 1}) \cdot \frac{180}{π}$

Rewrite the expression.

$\arctan (\frac{1 + \sqrt{2}}{1}) \cdot \frac{180}{π}$

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

$\arctan (1 + \sqrt{2}) \cdot \frac{180}{π}$

Step 4

Evaluate $\arctan (1 + \sqrt{2})$ .

$\frac{3 π}{8} \cdot \frac{180}{π}$

Step 5

Cancel the common factor of $π$ .

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Factor $π$ out of $3 π$ .

$\frac{π \cdot 3}{8} \cdot \frac{180}{π}$

Cancel the common factor.

$\frac{π \cdot 3}{8} \cdot \frac{180}{π}$

Rewrite the expression.

$\frac{3}{8} \cdot 180$

Step 6

Cancel the common factor of $4$ .

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Factor $4$ out of $8$ .

$\frac{3}{4 (2)} \cdot 180$

Factor $4$ out of $180$ .

$\frac{3}{4 \cdot 2} \cdot (4 \cdot 45)$

Cancel the common factor.

$\frac{3}{4 \cdot 2} \cdot (4 \cdot 45)$

Rewrite the expression.

$\frac{3}{2} \cdot 45$

Step 7

Combine $\frac{3}{2}$ and $45$ .

$\frac{3 \cdot 45}{2}$

Step 8

Multiply $3$ by $45$ .

$\frac{135}{2}$

Step 9

Convert to a decimal.

$67.5 °$