Trigonometry Examples

$\frac{1}{2 p \cdot \sqrt{100 \cdot 10^{- 3} \cdot 0.01 \cdot 10^{- 6}}}$

Step 1

Multiply $100$ by $0.01$ .

$\frac{1}{2 p \cdot \sqrt{1 (10^{- 3} \cdot 10^{- 6})}}$

Step 2

Multiply $10^{- 3}$ by $10^{- 6}$ by adding the exponents.

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Step 2.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{1}{2 p \cdot \sqrt{1 \cdot 10^{- 3 - 6}}}$

Step 2.2

Subtract $6$ from $- 3$ .

$\frac{1}{2 p \cdot \sqrt{1 \cdot 10^{- 9}}}$

Step 3

Rewrite $1 \cdot 10^{- 9}$ as $0.1 \cdot 10^{- 8}$ .

$\frac{1}{2 p \cdot \sqrt{0.1 \cdot 10^{- 8}}}$

Step 4

Rewrite $\sqrt{0.1 \cdot 10^{- 8}}$ as $\sqrt{0.1} \cdot \sqrt{10^{- 8}}$ .

$\frac{1}{2 p \cdot (\sqrt{0.1} \cdot \sqrt{10^{- 8}})}$

Step 5

Evaluate the root.

$\frac{1}{2 p \cdot (0.31622776 \cdot \sqrt{10^{- 8}})}$

Step 6

Rewrite $10^{- 8}$ as ${(10^{- 4})}^{2}$ .

$\frac{1}{2 p \cdot (0.31622776 \cdot \sqrt{{(10^{- 4})}^{2}})}$

Step 7

Pull terms out from under the radical, assuming positive real numbers.

$\frac{1}{2 p \cdot 0.31622776 \cdot 10^{- 4}}$

Step 8

Simplify the expression.

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Step 8.1

Move $10^{- 4}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{10^{4}}{2 p \cdot 0.31622776}$

Step 8.2

Raise $10$ to the power of $4$ .

$\frac{10000}{2 p \cdot 0.31622776}$

Step 8.3

Multiply $0.31622776$ by $2$ .

$\frac{10000}{0.63245553 p}$

Step 9

Factor $10000$ out of $10000$ .

$\frac{10000 (1)}{0.63245553 p}$

Step 10

Factor $0.63245553$ out of $0.63245553 p$ .

$\frac{10000 (1)}{0.63245553 (p)}$

Step 11

Separate fractions.

$\frac{10000}{0.63245553} \cdot \frac{1}{p}$

Step 12

Divide $10000$ by $0.63245553$ .

$15811.38830084 \frac{1}{p}$

Step 13

Combine $15811.38830084$ and $\frac{1}{p}$ .

$\frac{15811.38830084}{p}$