Trigonometry Examples

$5 ° 5' 5''$

Step 1

Since

$5$ is a whole number, it is a full degree. Since each minute is equal to

$\frac{1}{60}$ degree, multiply

$5$ by

$\frac{1}{60}$ . Since each second is equal to

$\frac{1}{3600}$ degree, multiply

$5$ by

$\frac{1}{3600}$ . Add them together.

$5 + 5 \cdot \frac{1}{60} + 5 \cdot \frac{1}{3600}$

Step 2

Simplify.

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Step 2.1

Remove parentheses.

$5 + 5 \cdot \frac{1}{60} + 5 \cdot \frac{1}{3600}$

Step 2.2

Simplify each term.

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Step 2.2.1

Cancel the common factor of

$5$ .

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Step 2.2.1.1

Factor

$5$ out of

$60$ .

$5 + 5 \cdot \frac{1}{5 (12)} + 5 \cdot \frac{1}{3600}$

Step 2.2.1.2

Cancel the common factor.

$5 + 5 \cdot \frac{1}{5 \cdot 12} + 5 \cdot \frac{1}{3600}$

Step 2.2.1.3

Rewrite the expression.

$5 + \frac{1}{12} + 5 \cdot \frac{1}{3600}$

Step 2.2.2

Cancel the common factor of

$5$ .

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Step 2.2.2.1

Factor

$5$ out of

$3600$ .

$5 + \frac{1}{12} + 5 \cdot \frac{1}{5 (720)}$

Step 2.2.2.2

Cancel the common factor.

$5 + \frac{1}{12} + 5 \cdot \frac{1}{5 \cdot 720}$

Step 2.2.2.3

Rewrite the expression.

$5 + \frac{1}{12} + \frac{1}{720}$

Step 2.3

Find the common denominator.

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Step 2.3.1

Write

$5$ as a fraction with denominator

$1$ .

$\frac{5}{1} + \frac{1}{12} + \frac{1}{720}$

Step 2.3.2

Multiply

$\frac{5}{1}$ by

$\frac{720}{720}$ .

$\frac{5}{1} \cdot \frac{720}{720} + \frac{1}{12} + \frac{1}{720}$

Step 2.3.3

Multiply

$\frac{5}{1}$ by

$\frac{720}{720}$ .

$\frac{5 \cdot 720}{720} + \frac{1}{12} + \frac{1}{720}$

Step 2.3.4

Multiply

$\frac{1}{12}$ by

$\frac{60}{60}$ .

$\frac{5 \cdot 720}{720} + \frac{1}{12} \cdot \frac{60}{60} + \frac{1}{720}$

Step 2.3.5

Multiply

$\frac{1}{12}$ by

$\frac{60}{60}$ .

$\frac{5 \cdot 720}{720} + \frac{60}{12 \cdot 60} + \frac{1}{720}$

Step 2.3.6

Multiply

$12$ by

$60$ .

$\frac{5 \cdot 720}{720} + \frac{60}{720} + \frac{1}{720}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{5 \cdot 720 + 60 + 1}{720}$

Step 2.5

Simplify the expression.

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Step 2.5.1

Multiply

$5$ by

$720$ .

$\frac{3600 + 60 + 1}{720}$

Step 2.5.2

Add

$3600$ and

$60$ .

$\frac{3660 + 1}{720}$

Step 2.5.3

Add

$3660$ and

$1$ .

$\frac{3661}{720}$

Step 3

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

$5.0847\overline{2} °$