Trigonometry Examples

$121 ° 22' 36''$

Step 1

Since $121$ is a whole number, it is a full degree. Since each minute is equal to $\frac{1}{60}$ degree, multiply $22$ by $\frac{1}{60}$ . Since each second is equal to $\frac{1}{3600}$ degree, multiply $36$ by $\frac{1}{3600}$ . Add them together.

$121 + 22 \cdot \frac{1}{60} + 36 \cdot \frac{1}{3600}$

Step 2

Simplify.

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Step 2.1

Remove parentheses.

$121 + 22 \cdot \frac{1}{60} + 36 \cdot \frac{1}{3600}$

Step 2.2

Simplify each term.

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Step 2.2.1

Cancel the common factor of $2$ .

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Step 2.2.1.1

Factor $2$ out of $22$ .

$121 + 2 (11) \cdot \frac{1}{60} + 36 \cdot \frac{1}{3600}$

Step 2.2.1.2

Factor $2$ out of $60$ .

$121 + 2 \cdot 11 \cdot \frac{1}{2 \cdot 30} + 36 \cdot \frac{1}{3600}$

Step 2.2.1.3

Cancel the common factor.

$121 + 2 \cdot 11 \cdot \frac{1}{2 \cdot 30} + 36 \cdot \frac{1}{3600}$

Step 2.2.1.4

Rewrite the expression.

$121 + 11 \cdot \frac{1}{30} + 36 \cdot \frac{1}{3600}$

Step 2.2.2

Combine $11$ and $\frac{1}{30}$ .

$121 + \frac{11}{30} + 36 \cdot \frac{1}{3600}$

Step 2.2.3

Cancel the common factor of $36$ .

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Step 2.2.3.1

Factor $36$ out of $3600$ .

$121 + \frac{11}{30} + 36 \cdot \frac{1}{36 (100)}$

Step 2.2.3.2

Cancel the common factor.

$121 + \frac{11}{30} + 36 \cdot \frac{1}{36 \cdot 100}$

Step 2.2.3.3

Rewrite the expression.

$121 + \frac{11}{30} + \frac{1}{100}$

Step 2.3

Find the common denominator.

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Step 2.3.1

Write $121$ as a fraction with denominator $1$ .

$\frac{121}{1} + \frac{11}{30} + \frac{1}{100}$

Step 2.3.2

Multiply $\frac{121}{1}$ by $\frac{300}{300}$ .

$\frac{121}{1} \cdot \frac{300}{300} + \frac{11}{30} + \frac{1}{100}$

Step 2.3.3

Multiply $\frac{121}{1}$ by $\frac{300}{300}$ .

$\frac{121 \cdot 300}{300} + \frac{11}{30} + \frac{1}{100}$

Step 2.3.4

Multiply $\frac{11}{30}$ by $\frac{10}{10}$ .

$\frac{121 \cdot 300}{300} + \frac{11}{30} \cdot \frac{10}{10} + \frac{1}{100}$

Step 2.3.5

Multiply $\frac{11}{30}$ by $\frac{10}{10}$ .

$\frac{121 \cdot 300}{300} + \frac{11 \cdot 10}{30 \cdot 10} + \frac{1}{100}$

Step 2.3.6

Multiply $\frac{1}{100}$ by $\frac{3}{3}$ .

$\frac{121 \cdot 300}{300} + \frac{11 \cdot 10}{30 \cdot 10} + \frac{1}{100} \cdot \frac{3}{3}$

Step 2.3.7

Multiply $\frac{1}{100}$ by $\frac{3}{3}$ .

$\frac{121 \cdot 300}{300} + \frac{11 \cdot 10}{30 \cdot 10} + \frac{3}{100 \cdot 3}$

Step 2.3.8

Reorder the factors of $30 \cdot 10$ .

$\frac{121 \cdot 300}{300} + \frac{11 \cdot 10}{10 \cdot 30} + \frac{3}{100 \cdot 3}$

Step 2.3.9

Multiply $10$ by $30$ .

$\frac{121 \cdot 300}{300} + \frac{11 \cdot 10}{300} + \frac{3}{100 \cdot 3}$

Step 2.3.10

Reorder the factors of $100 \cdot 3$ .

$\frac{121 \cdot 300}{300} + \frac{11 \cdot 10}{300} + \frac{3}{3 \cdot 100}$

Step 2.3.11

Multiply $3$ by $100$ .

$\frac{121 \cdot 300}{300} + \frac{11 \cdot 10}{300} + \frac{3}{300}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{121 \cdot 300 + 11 \cdot 10 + 3}{300}$

Step 2.5

Simplify each term.

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Step 2.5.1

Multiply $121$ by $300$ .

$\frac{36300 + 11 \cdot 10 + 3}{300}$

Step 2.5.2

Multiply $11$ by $10$ .

$\frac{36300 + 110 + 3}{300}$

Step 2.6

Simplify by adding numbers.

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Step 2.6.1

Add $36300$ and $110$ .

$\frac{36410 + 3}{300}$

Step 2.6.2

Add $36410$ and $3$ .

$\frac{36413}{300}$

Step 3

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

$121.37\overline{6} °$