Trigonometry Examples

$120.15' (36'')$

Step 1

Since $0$ is a whole number, it is a full degree. Since each minute is equal to $\frac{1}{60}$ degree, multiply $15$ by $\frac{1}{60}$ . Since each second is equal to $\frac{1}{3600}$ degree, multiply $36$ by $\frac{1}{3600}$ . Add them together.

$0 + 15 \cdot \frac{1}{60} + 36 \cdot \frac{1}{3600}$

Step 2

Simplify.

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Step 2.1

Remove parentheses.

$0 + 15 \cdot \frac{1}{60} + 36 \cdot \frac{1}{3600}$

Step 2.2

Simplify each term.

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Step 2.2.1

Cancel the common factor of $15$ .

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Step 2.2.1.1

Factor $15$ out of $60$ .

$0 + 15 \cdot \frac{1}{15 (4)} + 36 \cdot \frac{1}{3600}$

Step 2.2.1.2

Cancel the common factor.

$0 + 15 \cdot \frac{1}{15 \cdot 4} + 36 \cdot \frac{1}{3600}$

Step 2.2.1.3

Rewrite the expression.

$0 + \frac{1}{4} + 36 \cdot \frac{1}{3600}$

Step 2.2.2

Cancel the common factor of $36$ .

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Step 2.2.2.1

Factor $36$ out of $3600$ .

$0 + \frac{1}{4} + 36 \cdot \frac{1}{36 (100)}$

Step 2.2.2.2

Cancel the common factor.

$0 + \frac{1}{4} + 36 \cdot \frac{1}{36 \cdot 100}$

Step 2.2.2.3

Rewrite the expression.

$0 + \frac{1}{4} + \frac{1}{100}$

Step 2.3

Add $0$ and $\frac{1}{4}$ .

$\frac{1}{4} + \frac{1}{100}$

Step 2.4

To write $\frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{25}{25}$ .

$\frac{1}{4} \cdot \frac{25}{25} + \frac{1}{100}$

Step 2.5

Write each expression with a common denominator of $100$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.5.1

Multiply $\frac{1}{4}$ by $\frac{25}{25}$ .

$\frac{25}{4 \cdot 25} + \frac{1}{100}$

Step 2.5.2

Multiply $4$ by $25$ .

$\frac{25}{100} + \frac{1}{100}$

Step 2.6

Simplify the expression.

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Step 2.6.1

Combine the numerators over the common denominator.

$\frac{25 + 1}{100}$

Step 2.6.2

Add $25$ and $1$ .

$\frac{26}{100}$

Step 2.7

Cancel the common factor of $26$ and $100$ .

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Step 2.7.1

Factor $2$ out of $26$ .

$\frac{2 (13)}{100}$

Step 2.7.2

Cancel the common factors.

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Step 2.7.2.1

Factor $2$ out of $100$ .

$\frac{2 \cdot 13}{2 \cdot 50}$

Step 2.7.2.2

Cancel the common factor.

$\frac{2 \cdot 13}{2 \cdot 50}$

Step 2.7.2.3

Rewrite the expression.

$\frac{13}{50}$

Step 3

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

$0.26 °$