Trigonometry Examples

$54 ° 30'$

Step 1

Since

$54$ is a whole number, it is a full degree. Since each minute is equal to

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

$30$ by

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

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

$0$ by

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

$54 + 30 \cdot \frac{1}{60} + 0 \cdot \frac{1}{3600}$

Step 2

Simplify.

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Step 2.1

Remove parentheses.

$54 + 30 \cdot \frac{1}{60} + 0 \cdot \frac{1}{3600}$

Step 2.2

Simplify each term.

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Step 2.2.1

Cancel the common factor of

$30$ .

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Step 2.2.1.1

Factor

$30$ out of

$60$ .

$54 + 30 \cdot \frac{1}{30 (2)} + 0 \cdot \frac{1}{3600}$

Step 2.2.1.2

Cancel the common factor.

$54 + 30 \cdot \frac{1}{30 \cdot 2} + 0 \cdot \frac{1}{3600}$

Step 2.2.1.3

Rewrite the expression.

$54 + \frac{1}{2} + 0 \cdot \frac{1}{3600}$

Step 2.2.2

Multiply

$0$ by

$\frac{1}{3600}$ .

$54 + \frac{1}{2} + 0$

Step 2.3

To write

$54$ as a fraction with a common denominator, multiply by

$\frac{2}{2}$ .

$54 \cdot \frac{2}{2} + \frac{1}{2} + 0$

Step 2.4

Combine

$54$ and

$\frac{2}{2}$ .

$\frac{54 \cdot 2}{2} + \frac{1}{2} + 0$

Step 2.5

Combine the numerators over the common denominator.

$\frac{54 \cdot 2 + 1}{2} + 0$

Step 2.6

Simplify the numerator.

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Step 2.6.1

Multiply

$54$ by

$2$ .

$\frac{108 + 1}{2} + 0$

Step 2.6.2

Add

$108$ and

$1$ .

$\frac{109}{2} + 0$

Step 2.7

Add

$\frac{109}{2}$ and

$0$ .

$\frac{109}{2}$

Step 3

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

$54.5 °$