Trigonometry Examples

$\frac{120}{\tan (60)} + \frac{120}{\tan (60)}$

Step 1

Combine the numerators over the common denominator.

$\frac{120 + 120}{\tan (60)}$

Step 2

Add $120$ and $120$ .

$\frac{240}{\tan (60)}$

Step 3

Separate fractions.

$\frac{240}{1} \cdot \frac{1}{\tan (60)}$

Step 4

Rewrite $\tan (60)$ in terms of sines and cosines.

$\frac{240}{1} \cdot \frac{1}{\frac{\sin (60)}{\cos (60)}}$

Step 5

Multiply by the reciprocal of the fraction to divide by $\frac{\sin (60)}{\cos (60)}$ .

$\frac{240}{1} \cdot \frac{\cos (60)}{\sin (60)}$

Step 6

Convert from $\frac{\cos (60)}{\sin (60)}$ to $\cot (60)$ .

$\frac{240}{1} \cot (60)$

Step 7

Divide $240$ by $1$ .

$240 \cot (60)$

Step 8

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

$240 \frac{1}{\sqrt{3}}$

Step 9

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

$240 (\frac{1}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}})$

Step 10

Combine and simplify the denominator.

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Step 10.1

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

$240 \frac{\sqrt{3}}{\sqrt{3} \sqrt{3}}$

Step 10.2

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

$240 \frac{\sqrt{3}}{{\sqrt{3}}^{1} \sqrt{3}}$

Step 10.3

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

$240 \frac{\sqrt{3}}{{\sqrt{3}}^{1} {\sqrt{3}}^{1}}$

Step 10.4

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

$240 \frac{\sqrt{3}}{{\sqrt{3}}^{1 + 1}}$

Step 10.5

Add $1$ and $1$ .

$240 \frac{\sqrt{3}}{{\sqrt{3}}^{2}}$

Step 10.6

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

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Step 10.6.1

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

$240 \frac{\sqrt{3}}{{(3^{\frac{1}{2}})}^{2}}$

Step 10.6.2

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

$240 \frac{\sqrt{3}}{3^{\frac{1}{2} \cdot 2}}$

Step 10.6.3

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

$240 \frac{\sqrt{3}}{3^{\frac{2}{2}}}$

Step 10.6.4

Cancel the common factor of $2$ .

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Step 10.6.4.1

Cancel the common factor.

$240 \frac{\sqrt{3}}{3^{\frac{2}{2}}}$

Step 10.6.4.2

Rewrite the expression.

$240 \frac{\sqrt{3}}{3^{1}}$

Step 10.6.5

Evaluate the exponent.

$240 \frac{\sqrt{3}}{3}$

Step 11

Cancel the common factor of $3$ .

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Step 11.1

Factor $3$ out of $240$ .

$3 (80) \frac{\sqrt{3}}{3}$

Step 11.2

Cancel the common factor.

$3 \cdot 80 \frac{\sqrt{3}}{3}$

Step 11.3

Rewrite the expression.

$80 \sqrt{3}$

Step 12

The result can be shown in multiple forms.

Exact Form:

$80 \sqrt{3}$

Decimal Form:

$138.56406460 \dots$