Trigonometry Examples

$\tan^{2} (30)$

Step 1

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

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

Step 2

Apply the product rule to $\frac{\sqrt{3}}{3}$ .

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

Step 3

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

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Step 3.1

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

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

Step 3.2

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

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

Step 3.3

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

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

Step 3.4

Cancel the common factor of $2$ .

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Step 3.4.1

Cancel the common factor.

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

Step 3.4.2

Rewrite the expression.

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

Step 3.5

Evaluate the exponent.

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

Step 4

Raise $3$ to the power of $2$ .

$\frac{3}{9}$

Step 5

Cancel the common factor of $3$ and $9$ .

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Step 5.1

Factor $3$ out of $3$ .

$\frac{3 (1)}{9}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $3$ out of $9$ .

$\frac{3 \cdot 1}{3 \cdot 3}$

Step 5.2.2

Cancel the common factor.

$\frac{3 \cdot 1}{3 \cdot 3}$

Step 5.2.3

Rewrite the expression.

$\frac{1}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{3}$

Decimal Form:

$0.\overline{3}$