Trigonometry Examples

$7 ° 7' 7''$

Step 1

Since $7$ is a whole number, it is a full degree. Since each minute is equal to $\frac{1}{60}$ degree, multiply $7$ by $\frac{1}{60}$ . Since each second is equal to $\frac{1}{3600}$ degree, multiply $7$ by $\frac{1}{3600}$ . Add them together.

$7 + 7 \cdot \frac{1}{60} + 7 \cdot \frac{1}{3600}$

Step 2

Simplify.

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Step 2.1

Remove parentheses.

$7 + 7 \cdot \frac{1}{60} + 7 \cdot \frac{1}{3600}$

Step 2.2

Simplify each term.

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Step 2.2.1

Combine $7$ and $\frac{1}{60}$ .

$7 + \frac{7}{60} + 7 \cdot \frac{1}{3600}$

Step 2.2.2

Combine $7$ and $\frac{1}{3600}$ .

$7 + \frac{7}{60} + \frac{7}{3600}$

Step 2.3

Find the common denominator.

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Step 2.3.1

Write $7$ as a fraction with denominator $1$ .

$\frac{7}{1} + \frac{7}{60} + \frac{7}{3600}$

Step 2.3.2

Multiply $\frac{7}{1}$ by $\frac{3600}{3600}$ .

$\frac{7}{1} \cdot \frac{3600}{3600} + \frac{7}{60} + \frac{7}{3600}$

Step 2.3.3

Multiply $\frac{7}{1}$ by $\frac{3600}{3600}$ .

$\frac{7 \cdot 3600}{3600} + \frac{7}{60} + \frac{7}{3600}$

Step 2.3.4

Multiply $\frac{7}{60}$ by $\frac{60}{60}$ .

$\frac{7 \cdot 3600}{3600} + \frac{7}{60} \cdot \frac{60}{60} + \frac{7}{3600}$

Step 2.3.5

Multiply $\frac{7}{60}$ by $\frac{60}{60}$ .

$\frac{7 \cdot 3600}{3600} + \frac{7 \cdot 60}{60 \cdot 60} + \frac{7}{3600}$

Step 2.3.6

Multiply $60$ by $60$ .

$\frac{7 \cdot 3600}{3600} + \frac{7 \cdot 60}{3600} + \frac{7}{3600}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{7 \cdot 3600 + 7 \cdot 60 + 7}{3600}$

Step 2.5

Simplify each term.

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Step 2.5.1

Multiply $7$ by $3600$ .

$\frac{25200 + 7 \cdot 60 + 7}{3600}$

Step 2.5.2

Multiply $7$ by $60$ .

$\frac{25200 + 420 + 7}{3600}$

Step 2.6

Simplify by adding numbers.

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Step 2.6.1

Add $25200$ and $420$ .

$\frac{25620 + 7}{3600}$

Step 2.6.2

Add $25620$ and $7$ .

$\frac{25627}{3600}$

Step 3

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

$7.1186\overline{1} °$