Trigonometry Examples

$\frac{22}{\cos (30)}$

Step 1

Separate fractions.

$\frac{22}{1} \cdot \frac{1}{\cos (30)}$

Step 2

Convert from $\frac{1}{\cos (30)}$ to $\sec (30)$ .

$\frac{22}{1} \sec (30)$

Step 3

Divide $22$ by $1$ .

$22 \sec (30)$

Step 4

The exact value of $\sec (30)$ is $\frac{2}{\sqrt{3}}$ .

$22 \frac{2}{\sqrt{3}}$

Step 5

Multiply $\frac{2}{\sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$22 (\frac{2}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}})$

Step 6

Combine and simplify the denominator.

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Step 6.1

Multiply $\frac{2}{\sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$22 \frac{2 \sqrt{3}}{\sqrt{3} \sqrt{3}}$

Step 6.2

Raise $\sqrt{3}$ to the power of $1$ .

$22 \frac{2 \sqrt{3}}{{\sqrt{3}}^{1} \sqrt{3}}$

Step 6.3

Raise $\sqrt{3}$ to the power of $1$ .

$22 \frac{2 \sqrt{3}}{{\sqrt{3}}^{1} {\sqrt{3}}^{1}}$

Step 6.4

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

$22 \frac{2 \sqrt{3}}{{\sqrt{3}}^{1 + 1}}$

Step 6.5

Add $1$ and $1$ .

$22 \frac{2 \sqrt{3}}{{\sqrt{3}}^{2}}$

Step 6.6

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

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Step 6.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$22 \frac{2 \sqrt{3}}{{(3^{\frac{1}{2}})}^{2}}$

Step 6.6.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$22 \frac{2 \sqrt{3}}{3^{\frac{1}{2} \cdot 2}}$

Step 6.6.3

Combine $\frac{1}{2}$ and $2$ .

$22 \frac{2 \sqrt{3}}{3^{\frac{2}{2}}}$

Step 6.6.4

Cancel the common factor of $2$ .

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Step 6.6.4.1

Cancel the common factor.

$22 \frac{2 \sqrt{3}}{3^{\frac{2}{2}}}$

Step 6.6.4.2

Rewrite the expression.

$22 \frac{2 \sqrt{3}}{3^{1}}$

Step 6.6.5

Evaluate the exponent.

$22 \frac{2 \sqrt{3}}{3}$

Step 7

Multiply $22 \frac{2 \sqrt{3}}{3}$ .

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Step 7.1

Combine $22$ and $\frac{2 \sqrt{3}}{3}$ .

$\frac{22 (2 \sqrt{3})}{3}$

Step 7.2

Multiply $2$ by $22$ .

$\frac{44 \sqrt{3}}{3}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{44 \sqrt{3}}{3}$

Decimal Form:

$25.40341184 \dots$