Trigonometry Examples

$A = \frac{1}{2} \cdot {(40)}^{2} \cdot \frac{2 π}{3}$

Step 1

Remove parentheses.

$A = \frac{1}{2} \cdot 40^{2} \cdot \frac{2 π}{3}$

Step 2

Simplify $\frac{1}{2} \cdot 40^{2} \cdot \frac{2 π}{3}$ .

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Step 2.1

Raise $40$ to the power of $2$ .

$A = \frac{1}{2} \cdot 1600 \cdot \frac{2 π}{3}$

Step 2.2

Cancel the common factor of $2$ .

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Step 2.2.1

Factor $2$ out of $1600$ .

$A = \frac{1}{2} \cdot (2 (800)) \cdot \frac{2 π}{3}$

Step 2.2.2

Cancel the common factor.

$A = \frac{1}{2} \cdot (2 \cdot 800) \cdot \frac{2 π}{3}$

Step 2.2.3

Rewrite the expression.

$A = 800 \cdot \frac{2 π}{3}$

Step 2.3

Multiply $800 \frac{2 π}{3}$ .

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Step 2.3.1

Combine $800$ and $\frac{2 π}{3}$ .

$A = \frac{800 (2 π)}{3}$

Step 2.3.2

Multiply $2$ by $800$ .

$A = \frac{1600 π}{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$A = \frac{1600 π}{3}$

Decimal Form:

$A = 1675.51608191 \dots$