Trigonometry Examples

\tan (60)

$\tan (60)$

Step 1

The angle

60

$60$ is an angle where the values of the six trigonometric functions are known. Because this is the case, add

0

$0$ to keep the value the same.

\tan (60 + 0)

$\tan (60 + 0)$

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)}

$\tan (A + B) = \frac{\tan (A) + \tan (B)}{1 - \tan (A) \tan (B)}$ .

\frac{\tan (60) + \tan (0)}{1 - \tan (60) \tan (0)}

$\frac{\tan (60) + \tan (0)}{1 - \tan (60) \tan (0)}$

Step 3

Simplify the numerator.

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Step 3.1

The exact value of

\tan (60)

$\tan (60)$ is

\sqrt{3}

$\sqrt{3}$ .

\frac{\sqrt{3} + \tan (0)}{1 - \tan (60) \tan (0)}

$\frac{\sqrt{3} + \tan (0)}{1 - \tan (60) \tan (0)}$

Step 3.2

The exact value of

\tan (0)

$\tan (0)$ is

0

$0$ .

\frac{\sqrt{3} + 0}{1 - \tan (60) \tan (0)}

$\frac{\sqrt{3} + 0}{1 - \tan (60) \tan (0)}$

Step 3.3

Add

\sqrt{3}

$\sqrt{3}$ and

0

$0$ .

\frac{\sqrt{3}}{1 - \tan (60) \tan (0)}

$\frac{\sqrt{3}}{1 - \tan (60) \tan (0)}$

\frac{\sqrt{3}}{1 - \tan (60) \tan (0)}

$\frac{\sqrt{3}}{1 - \tan (60) \tan (0)}$

Step 4

Simplify the denominator.

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Step 4.1

The exact value of

\tan (60)

$\tan (60)$ is

\sqrt{3}

$\sqrt{3}$ .

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

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

Step 4.2

The exact value of

\tan (0)

$\tan (0)$ is

0

$0$ .

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

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

Step 4.3

Multiply

- \sqrt{3} \cdot 0

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

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Step 4.3.1

Multiply

0

$0$ by

- 1

$- 1$ .

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

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

Step 4.3.2

Multiply

0

$0$ by

\sqrt{3}

$\sqrt{3}$ .

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

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

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

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

Step 4.4

Add

1

$1$ and

0

$0$ .

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

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

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

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

Step 5

Divide

\sqrt{3}

$\sqrt{3}$ by

1

$1$ .

\sqrt{3}

$\sqrt{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

\sqrt{3}

$\sqrt{3}$

Decimal Form:

1.73205080 \dots

$1.73205080 \dots$