Trigonometry Examples

$\arccos (\frac{450^{2} + 350^{2} - 200^{2}}{2 (450) \cdot (350)})$

Step 1

Simplify the numerator.

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Step 1.1

Raise $450$ to the power of $2$ .

$\arccos (\frac{202500 + 350^{2} - 200^{2}}{2 (450) \cdot 350})$

Step 1.2

Raise $350$ to the power of $2$ .

$\arccos (\frac{202500 + 122500 - 200^{2}}{2 (450) \cdot 350})$

Step 1.3

Raise $200$ to the power of $2$ .

$\arccos (\frac{202500 + 122500 - 1 \cdot 40000}{2 (450) \cdot 350})$

Step 1.4

Multiply $- 1$ by $40000$ .

$\arccos (\frac{202500 + 122500 - 40000}{2 (450) \cdot 350})$

Step 1.5

Add $202500$ and $122500$ .

$\arccos (\frac{325000 - 40000}{2 (450) \cdot 350})$

Step 1.6

Subtract $40000$ from $325000$ .

$\arccos (\frac{285000}{2 (450) \cdot 350})$

Step 2

Simplify the denominator.

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Step 2.1

Multiply $2$ by $450$ .

$\arccos (\frac{285000}{900 \cdot 350})$

Step 2.2

Multiply $900$ by $350$ .

$\arccos (\frac{285000}{315000})$

Step 3

Cancel the common factor of $285000$ and $315000$ .

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Step 3.1

Factor $15000$ out of $285000$ .

$\arccos (\frac{15000 (19)}{315000})$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $15000$ out of $315000$ .

$\arccos (\frac{15000 \cdot 19}{15000 \cdot 21})$

Step 3.2.2

Cancel the common factor.

$\arccos (\frac{15000 \cdot 19}{15000 \cdot 21})$

Step 3.2.3

Rewrite the expression.

$\arccos (\frac{19}{21})$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\arccos (\frac{19}{21})$

Decimal Form:

$0.43997595 \dots$