Trigonometry Examples

$\tan^{2} (60)$

Step 1

The exact value of $\tan (60)$ is $\sqrt{3}$ .

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

Step 2

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

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

Cancel the common factor of $2$ .

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Step 2.4.1

Cancel the common factor.

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

Step 2.4.2

Rewrite the expression.

$3^{1}$

Step 2.5

Evaluate the exponent.

$3$