Trigonometry Examples

$\arccos (1 - \frac{1440^{2}}{2 {(2220)}^{2}})$

Step 1

Simplify each term.

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Step 1.1

Raise $1440$ to the power of $2$ .

$\arccos (1 - \frac{2073600}{2 \cdot 2220^{2}})$

Step 1.2

Raise $2220$ to the power of $2$ .

$\arccos (1 - \frac{2073600}{2 \cdot 4928400})$

Step 1.3

Multiply $2$ by $4928400$ .

$\arccos (1 - \frac{2073600}{9856800})$

Step 1.4

Cancel the common factor of $2073600$ and $9856800$ .

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Step 1.4.1

Factor $7200$ out of $2073600$ .

$\arccos (1 - \frac{7200 (288)}{9856800})$

Step 1.4.2

Cancel the common factors.

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Step 1.4.2.1

Factor $7200$ out of $9856800$ .

$\arccos (1 - \frac{7200 \cdot 288}{7200 \cdot 1369})$

Step 1.4.2.2

Cancel the common factor.

$\arccos (1 - \frac{7200 \cdot 288}{7200 \cdot 1369})$

Step 1.4.2.3

Rewrite the expression.

$\arccos (1 - \frac{288}{1369})$

Step 2

Simplify the expression.

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Step 2.1

Write $1$ as a fraction with a common denominator.

$\arccos (\frac{1369}{1369} - \frac{288}{1369})$

Step 2.2

Combine the numerators over the common denominator.

$\arccos (\frac{1369 - 288}{1369})$

Step 2.3

Subtract $288$ from $1369$ .

$\arccos (\frac{1081}{1369})$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\arccos (\frac{1081}{1369})$

Decimal Form:

$0.66059470 \dots$