Calculus Examples

$\arctan (1) - \arctan (- 1)$

Step 1

Simplify each term.

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Step 1.1

The exact value of $\arctan (1)$ is $\frac{π}{4}$ .

$\frac{π}{4} - \arctan (- 1)$

Step 1.2

The exact value of $\arctan (- 1)$ is $- \frac{π}{4}$ .

$\frac{π}{4} - - \frac{π}{4}$

Step 1.3

Multiply $- - \frac{π}{4}$ .

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Step 1.3.1

Multiply $- 1$ by $- 1$ .

$\frac{π}{4} + 1 \frac{π}{4}$

Step 1.3.2

Multiply $\frac{π}{4}$ by $1$ .

$\frac{π}{4} + \frac{π}{4}$

Step 2

Simplify terms.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{π + π}{4}$

Step 2.2

Add $π$ and $π$ .

$\frac{2 π}{4}$

Step 2.3

Cancel the common factor of $2$ and $4$ .

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Step 2.3.1

Factor $2$ out of $2 π$ .

$\frac{2 (π)}{4}$

Step 2.3.2

Cancel the common factors.

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Step 2.3.2.1

Factor $2$ out of $4$ .

$\frac{2 π}{2 \cdot 2}$

Step 2.3.2.2

Cancel the common factor.

$\frac{2 π}{2 \cdot 2}$

Step 2.3.2.3

Rewrite the expression.

$\frac{π}{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{π}{2}$

Decimal Form:

$1.57079632 \dots$