Trigonometry Examples

$125 ° 50'$

Step 1

Since $125$ is a whole number, it is a full degree. Since each minute is equal to $\frac{1}{60}$ degree, multiply $50$ by $\frac{1}{60}$ . Since each second is equal to $\frac{1}{3600}$ degree, multiply $0$ by $\frac{1}{3600}$ . Add them together.

$125 + 50 \cdot \frac{1}{60} + 0 \cdot \frac{1}{3600}$

Step 2

Simplify.

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Step 2.1

Remove parentheses.

$125 + 50 \cdot \frac{1}{60} + 0 \cdot \frac{1}{3600}$

Step 2.2

Simplify each term.

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Step 2.2.1

Cancel the common factor of $10$ .

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Step 2.2.1.1

Factor $10$ out of $50$ .

$125 + 10 (5) \cdot \frac{1}{60} + 0 \cdot \frac{1}{3600}$

Step 2.2.1.2

Factor $10$ out of $60$ .

$125 + 10 \cdot 5 \cdot \frac{1}{10 \cdot 6} + 0 \cdot \frac{1}{3600}$

Step 2.2.1.3

Cancel the common factor.

$125 + 10 \cdot 5 \cdot \frac{1}{10 \cdot 6} + 0 \cdot \frac{1}{3600}$

Step 2.2.1.4

Rewrite the expression.

$125 + 5 \cdot \frac{1}{6} + 0 \cdot \frac{1}{3600}$

Step 2.2.2

Combine $5$ and $\frac{1}{6}$ .

$125 + \frac{5}{6} + 0 \cdot \frac{1}{3600}$

Step 2.2.3

Multiply $0$ by $\frac{1}{3600}$ .

$125 + \frac{5}{6} + 0$

Step 2.3

To write $125$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$125 \cdot \frac{6}{6} + \frac{5}{6} + 0$

Step 2.4

Combine $125$ and $\frac{6}{6}$ .

$\frac{125 \cdot 6}{6} + \frac{5}{6} + 0$

Step 2.5

Combine the numerators over the common denominator.

$\frac{125 \cdot 6 + 5}{6} + 0$

Step 2.6

Simplify the numerator.

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Step 2.6.1

Multiply $125$ by $6$ .

$\frac{750 + 5}{6} + 0$

Step 2.6.2

Add $750$ and $5$ .

$\frac{755}{6} + 0$

Step 2.7

Add $\frac{755}{6}$ and $0$ .

$\frac{755}{6}$

Step 3

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

$125.8\overline{3} °$