Precalculus Examples

$\cot (60)$

Step 1

To convert degrees to radians, multiply by $\frac{π}{180 °}$ , since a full circle is $360 °$ or $2 π$ radians.

Step 2

The exact value of $\cot (60)$ is $\frac{1}{\sqrt{3}}$ .

$\frac{1}{\sqrt{3}} \cdot \frac{π}{180}$ radians

Step 3

Multiply $\frac{1}{\sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$\frac{1}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} \cdot \frac{π}{180}$ radians

Step 4

Combine and simplify the denominator.

Tap for more steps...

Step 4.1

Multiply $\frac{1}{\sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$\frac{\sqrt{3}}{\sqrt{3} \sqrt{3}} \cdot \frac{π}{180}$ radians

Step 4.2

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

$\frac{\sqrt{3}}{\sqrt{3} \sqrt{3}} \cdot \frac{π}{180}$ radians

Step 4.3

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

$\frac{\sqrt{3}}{\sqrt{3} \sqrt{3}} \cdot \frac{π}{180}$ radians

Step 4.4

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

$\frac{\sqrt{3}}{{\sqrt{3}}^{1 + 1}} \cdot \frac{π}{180}$ radians

Step 4.5

Add $1$ and $1$ .

$\frac{\sqrt{3}}{{\sqrt{3}}^{2}} \cdot \frac{π}{180}$ radians

Step 4.6

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

Tap for more steps...

Step 4.6.1

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

$\frac{\sqrt{3}}{{(3^{\frac{1}{2}})}^{2}} \cdot \frac{π}{180}$ radians

Step 4.6.2

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

$\frac{\sqrt{3}}{3^{\frac{1}{2} \cdot 2}} \cdot \frac{π}{180}$ radians

Step 4.6.3

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

$\frac{\sqrt{3}}{3^{\frac{2}{2}}} \cdot \frac{π}{180}$ radians

Step 4.6.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 4.6.4.1

Cancel the common factor.

$\frac{\sqrt{3}}{3^{\frac{2}{2}}} \cdot \frac{π}{180}$ radians

Step 4.6.4.2

Rewrite the expression.

$\frac{\sqrt{3}}{3} \cdot \frac{π}{180}$ radians

Step 4.6.5

Evaluate the exponent.

$\frac{\sqrt{3}}{3} \cdot \frac{π}{180}$ radians

Step 5

Multiply $\frac{\sqrt{3}}{3} \cdot \frac{π}{180}$ .

Tap for more steps...

Step 5.1

Multiply $\frac{\sqrt{3}}{3}$ by $\frac{π}{180}$ .

$\frac{\sqrt{3} π}{3 \cdot 180}$ radians

Step 5.2

Multiply $3$ by $180$ .

$\frac{\sqrt{3} π}{540}$ radians