Trigonometry Examples

$5 ° 55' 59''$

Step 1

Since $5$ is a whole number, it is a full degree. Since each minute is equal to $\frac{1}{60}$ degree, multiply $55$ by $\frac{1}{60}$ . Since each second is equal to $\frac{1}{3600}$ degree, multiply $59$ by $\frac{1}{3600}$ . Add them together.

$5 + 55 \cdot \frac{1}{60} + 59 \cdot \frac{1}{3600}$

Step 2

Simplify.

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Step 2.1

Remove parentheses.

$5 + 55 \cdot \frac{1}{60} + 59 \cdot \frac{1}{3600}$

Step 2.2

Simplify each term.

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Step 2.2.1

Cancel the common factor of $5$ .

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Step 2.2.1.1

Factor $5$ out of $55$ .

$5 + 5 (11) \cdot \frac{1}{60} + 59 \cdot \frac{1}{3600}$

Step 2.2.1.2

Factor $5$ out of $60$ .

$5 + 5 \cdot 11 \cdot \frac{1}{5 \cdot 12} + 59 \cdot \frac{1}{3600}$

Step 2.2.1.3

Cancel the common factor.

$5 + 5 \cdot 11 \cdot \frac{1}{5 \cdot 12} + 59 \cdot \frac{1}{3600}$

Step 2.2.1.4

Rewrite the expression.

$5 + 11 \cdot \frac{1}{12} + 59 \cdot \frac{1}{3600}$

Step 2.2.2

Combine $11$ and $\frac{1}{12}$ .

$5 + \frac{11}{12} + 59 \cdot \frac{1}{3600}$

Step 2.2.3

Combine $59$ and $\frac{1}{3600}$ .

$5 + \frac{11}{12} + \frac{59}{3600}$

Step 2.3

Find the common denominator.

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Step 2.3.1

Write $5$ as a fraction with denominator $1$ .

$\frac{5}{1} + \frac{11}{12} + \frac{59}{3600}$

Step 2.3.2

Multiply $\frac{5}{1}$ by $\frac{3600}{3600}$ .

$\frac{5}{1} \cdot \frac{3600}{3600} + \frac{11}{12} + \frac{59}{3600}$

Step 2.3.3

Multiply $\frac{5}{1}$ by $\frac{3600}{3600}$ .

$\frac{5 \cdot 3600}{3600} + \frac{11}{12} + \frac{59}{3600}$

Step 2.3.4

Multiply $\frac{11}{12}$ by $\frac{300}{300}$ .

$\frac{5 \cdot 3600}{3600} + \frac{11}{12} \cdot \frac{300}{300} + \frac{59}{3600}$

Step 2.3.5

Multiply $\frac{11}{12}$ by $\frac{300}{300}$ .

$\frac{5 \cdot 3600}{3600} + \frac{11 \cdot 300}{12 \cdot 300} + \frac{59}{3600}$

Step 2.3.6

Multiply $12$ by $300$ .

$\frac{5 \cdot 3600}{3600} + \frac{11 \cdot 300}{3600} + \frac{59}{3600}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{5 \cdot 3600 + 11 \cdot 300 + 59}{3600}$

Step 2.5

Simplify each term.

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Step 2.5.1

Multiply $5$ by $3600$ .

$\frac{18000 + 11 \cdot 300 + 59}{3600}$

Step 2.5.2

Multiply $11$ by $300$ .

$\frac{18000 + 3300 + 59}{3600}$

Step 2.6

Simplify by adding numbers.

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Step 2.6.1

Add $18000$ and $3300$ .

$\frac{21300 + 59}{3600}$

Step 2.6.2

Add $21300$ and $59$ .

$\frac{21359}{3600}$

Step 3

Convert the fraction to a decimal by dividing the numerator by the denominator.

$5.9330\overline{5} °$