Trigonometry Examples

$664' (19'')$

Step 1

Since $0$ is a whole number, it is a full degree. Since each minute is equal to $\frac{1}{60}$ degree, multiply $664$ by $\frac{1}{60}$ . Since each second is equal to $\frac{1}{3600}$ degree, multiply $19$ by $\frac{1}{3600}$ . Add them together.

$0 + 664 \cdot \frac{1}{60} + 19 \cdot \frac{1}{3600}$

Step 2

Simplify.

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Step 2.1

Remove parentheses.

$0 + 664 \cdot \frac{1}{60} + 19 \cdot \frac{1}{3600}$

Step 2.2

Simplify each term.

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Step 2.2.1

Cancel the common factor of $4$ .

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Step 2.2.1.1

Factor $4$ out of $664$ .

$0 + 4 (166) \cdot \frac{1}{60} + 19 \cdot \frac{1}{3600}$

Step 2.2.1.2

Factor $4$ out of $60$ .

$0 + 4 \cdot 166 \cdot \frac{1}{4 \cdot 15} + 19 \cdot \frac{1}{3600}$

Step 2.2.1.3

Cancel the common factor.

$0 + 4 \cdot 166 \cdot \frac{1}{4 \cdot 15} + 19 \cdot \frac{1}{3600}$

Step 2.2.1.4

Rewrite the expression.

$0 + 166 \cdot \frac{1}{15} + 19 \cdot \frac{1}{3600}$

Step 2.2.2

Combine $166$ and $\frac{1}{15}$ .

$0 + \frac{166}{15} + 19 \cdot \frac{1}{3600}$

Step 2.2.3

Combine $19$ and $\frac{1}{3600}$ .

$0 + \frac{166}{15} + \frac{19}{3600}$

Step 2.3

Add $0$ and $\frac{166}{15}$ .

$\frac{166}{15} + \frac{19}{3600}$

Step 2.4

To write $\frac{166}{15}$ as a fraction with a common denominator, multiply by $\frac{240}{240}$ .

$\frac{166}{15} \cdot \frac{240}{240} + \frac{19}{3600}$

Step 2.5

Write each expression with a common denominator of $3600$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.5.1

Multiply $\frac{166}{15}$ by $\frac{240}{240}$ .

$\frac{166 \cdot 240}{15 \cdot 240} + \frac{19}{3600}$

Step 2.5.2

Multiply $15$ by $240$ .

$\frac{166 \cdot 240}{3600} + \frac{19}{3600}$

Step 2.6

Combine the numerators over the common denominator.

$\frac{166 \cdot 240 + 19}{3600}$

Step 2.7

Simplify the numerator.

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Step 2.7.1

Multiply $166$ by $240$ .

$\frac{39840 + 19}{3600}$

Step 2.7.2

Add $39840$ and $19$ .

$\frac{39859}{3600}$

Step 3

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

$11.0719\overline{4} °$