Trigonometry Examples

$13' (56'')$

Step 1

Since $0$ is a whole number, it is a full degree. Since each minute is equal to $\frac{1}{60}$ degree, multiply $13$ by $\frac{1}{60}$ . Since each second is equal to $\frac{1}{3600}$ degree, multiply $56$ by $\frac{1}{3600}$ . Add them together.

$0 + 13 \cdot \frac{1}{60} + 56 \cdot \frac{1}{3600}$

Step 2

Simplify.

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Step 2.1

Remove parentheses.

$0 + 13 \cdot \frac{1}{60} + 56 \cdot \frac{1}{3600}$

Step 2.2

Simplify each term.

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Step 2.2.1

Combine $13$ and $\frac{1}{60}$ .

$0 + \frac{13}{60} + 56 \cdot \frac{1}{3600}$

Step 2.2.2

Cancel the common factor of $8$ .

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Step 2.2.2.1

Factor $8$ out of $56$ .

$0 + \frac{13}{60} + 8 (7) \cdot \frac{1}{3600}$

Step 2.2.2.2

Factor $8$ out of $3600$ .

$0 + \frac{13}{60} + 8 \cdot 7 \cdot \frac{1}{8 \cdot 450}$

Step 2.2.2.3

Cancel the common factor.

$0 + \frac{13}{60} + 8 \cdot 7 \cdot \frac{1}{8 \cdot 450}$

Step 2.2.2.4

Rewrite the expression.

$0 + \frac{13}{60} + 7 \cdot \frac{1}{450}$

Step 2.2.3

Combine $7$ and $\frac{1}{450}$ .

$0 + \frac{13}{60} + \frac{7}{450}$

Step 2.3

Add $0$ and $\frac{13}{60}$ .

$\frac{13}{60} + \frac{7}{450}$

Step 2.4

To write $\frac{13}{60}$ as a fraction with a common denominator, multiply by $\frac{15}{15}$ .

$\frac{13}{60} \cdot \frac{15}{15} + \frac{7}{450}$

Step 2.5

To write $\frac{7}{450}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{13}{60} \cdot \frac{15}{15} + \frac{7}{450} \cdot \frac{2}{2}$

Step 2.6

Write each expression with a common denominator of $900$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.6.1

Multiply $\frac{13}{60}$ by $\frac{15}{15}$ .

$\frac{13 \cdot 15}{60 \cdot 15} + \frac{7}{450} \cdot \frac{2}{2}$

Step 2.6.2

Multiply $60$ by $15$ .

$\frac{13 \cdot 15}{900} + \frac{7}{450} \cdot \frac{2}{2}$

Step 2.6.3

Multiply $\frac{7}{450}$ by $\frac{2}{2}$ .

$\frac{13 \cdot 15}{900} + \frac{7 \cdot 2}{450 \cdot 2}$

Step 2.6.4

Multiply $450$ by $2$ .

$\frac{13 \cdot 15}{900} + \frac{7 \cdot 2}{900}$

Step 2.7

Combine the numerators over the common denominator.

$\frac{13 \cdot 15 + 7 \cdot 2}{900}$

Step 2.8

Simplify the numerator.

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Step 2.8.1

Multiply $13$ by $15$ .

$\frac{195 + 7 \cdot 2}{900}$

Step 2.8.2

Multiply $7$ by $2$ .

$\frac{195 + 14}{900}$

Step 2.8.3

Add $195$ and $14$ .

$\frac{209}{900}$

Step 3

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

$0.23\overline{2} °$