Trigonometry Examples

$P (8) = 10 (\tan (\frac{360}{2 n})) (2 n)$

Step 1

Simplify.

Tap for more steps...

Step 1.1

Reduce the expression $\frac{360}{2 n}$ by cancelling the common factors.

Tap for more steps...

Step 1.1.1

Factor $2$ out of $360$ .

$P (8) = 10 \tan (\frac{2 \cdot 180}{2 n}) (2 n)$

Step 1.1.2

Factor $2$ out of $2 n$ .

$P (8) = 10 \tan (\frac{2 \cdot 180}{2 (n)}) (2 n)$

Step 1.1.3

Cancel the common factor.

$P (8) = 10 \tan (\frac{2 \cdot 180}{2 n}) (2 n)$

Step 1.1.4

Rewrite the expression.

$P (8) = 10 \tan (\frac{180}{n}) (2 n)$

Step 1.2

Multiply $2$ by $10$ .

$P (8) = 20 \tan (\frac{180}{n}) n$

Step 2

Divide each term in $P (8) = 20 \tan (\frac{180}{n}) n$ by $8$ and simplify.

Tap for more steps...

Step 2.1

Divide each term in $P (8) = 20 \tan (\frac{180}{n}) n$ by $8$ .

$\frac{P (8)}{8} = \frac{20 \tan (\frac{180}{n}) n}{8}$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Cancel the common factor of $8$ .

Tap for more steps...

Step 2.2.1.1

Cancel the common factor.

$\frac{P \cdot 8}{8} = \frac{20 \tan (\frac{180}{n}) n}{8}$

Step 2.2.1.2

Divide $P$ by $1$ .

$P = \frac{20 \tan (\frac{180}{n}) n}{8}$

Step 2.3

Simplify the right side.

Tap for more steps...

Step 2.3.1

Cancel the common factor of $20$ and $8$ .

Tap for more steps...

Step 2.3.1.1

Factor $4$ out of $20 \tan (\frac{180}{n}) n$ .

$P = \frac{4 (5 \tan (\frac{180}{n}) n)}{8}$

Step 2.3.1.2

Cancel the common factors.

Tap for more steps...

Step 2.3.1.2.1

Factor $4$ out of $8$ .

$P = \frac{4 (5 \tan (\frac{180}{n}) n)}{4 (2)}$

Step 2.3.1.2.2

Cancel the common factor.

$P = \frac{4 (5 \tan (\frac{180}{n}) n)}{4 \cdot 2}$

Step 2.3.1.2.3

Rewrite the expression.

$P = \frac{5 \tan (\frac{180}{n}) n}{2}$

Step 2.3.2

Reorder factors in $\frac{5 \tan (\frac{180}{n}) n}{2}$ .

$P = \frac{5 n \tan (\frac{180}{n})}{2}$