Trigonometry Examples

$\tan (\frac{π}{6})$

Step 1

The angle $\frac{π}{6}$ is an angle where the values of the six trigonometric functions are known. Because this is the case, add $0$ to keep the value the same.

$\tan (\frac{π}{6} + 0)$

Step 2

Use the sum formula for tangent to simplify the expression. The formula states that $\tan (A + B) = \frac{\tan (A) + \tan (B)}{1 - \tan (A) \tan (B)}$ .

$\frac{\tan (\frac{π}{6}) + \tan (0)}{1 - \tan (\frac{π}{6}) \tan (0)}$

Step 3

Simplify the numerator.

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Step 3.1

The exact value of $\tan (\frac{π}{6})$ is $\frac{\sqrt{3}}{3}$ .

$\frac{\frac{\sqrt{3}}{3} + \tan (0)}{1 - \tan (\frac{π}{6}) \tan (0)}$

Step 3.2

The exact value of $\tan (0)$ is $0$ .

$\frac{\frac{\sqrt{3}}{3} + 0}{1 - \tan (\frac{π}{6}) \tan (0)}$

Step 3.3

Add $\frac{\sqrt{3}}{3}$ and $0$ .

$\frac{\frac{\sqrt{3}}{3}}{1 - \tan (\frac{π}{6}) \tan (0)}$

Step 4

Simplify the denominator.

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Step 4.1

The exact value of $\tan (\frac{π}{6})$ is $\frac{\sqrt{3}}{3}$ .

$\frac{\frac{\sqrt{3}}{3}}{1 - \frac{\sqrt{3}}{3} \tan (0)}$

Step 4.2

The exact value of $\tan (0)$ is $0$ .

$\frac{\frac{\sqrt{3}}{3}}{1 - \frac{\sqrt{3}}{3} \cdot 0}$

Step 4.3

Multiply $- \frac{\sqrt{3}}{3} \cdot 0$ .

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Step 4.3.1

Multiply $0$ by $- 1$ .

$\frac{\frac{\sqrt{3}}{3}}{1 + 0 \frac{\sqrt{3}}{3}}$

Step 4.3.2

Multiply $0$ by $\frac{\sqrt{3}}{3}$ .

$\frac{\frac{\sqrt{3}}{3}}{1 + 0}$

Step 4.4

Add $1$ and $0$ .

$\frac{\frac{\sqrt{3}}{3}}{1}$

Step 5

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

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.57735026 \dots$