Trigonometry Examples

$11' 43''$

Step 1

Since $0$ is a whole number, it is a full degree. Since each minute is equal to $\frac{1}{60}$ degree, multiply $11$ by $\frac{1}{60}$ . Since each second is equal to $\frac{1}{3600}$ degree, multiply $43$ by $\frac{1}{3600}$ . Add them together.

$0 + 11 \cdot \frac{1}{60} + 43 \cdot \frac{1}{3600}$

Step 2

Simplify.

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Step 2.1

Remove parentheses.

$0 + 11 \cdot \frac{1}{60} + 43 \cdot \frac{1}{3600}$

Step 2.2

Simplify each term.

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Step 2.2.1

Combine $11$ and $\frac{1}{60}$ .

$0 + \frac{11}{60} + 43 \cdot \frac{1}{3600}$

Step 2.2.2

Combine $43$ and $\frac{1}{3600}$ .

$0 + \frac{11}{60} + \frac{43}{3600}$

Step 2.3

Add $0$ and $\frac{11}{60}$ .

$\frac{11}{60} + \frac{43}{3600}$

Step 2.4

To write $\frac{11}{60}$ as a fraction with a common denominator, multiply by $\frac{60}{60}$ .

$\frac{11}{60} \cdot \frac{60}{60} + \frac{43}{3600}$

Step 2.5

Write each expression with a common denominator of $3600$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.5.1

Multiply $\frac{11}{60}$ by $\frac{60}{60}$ .

$\frac{11 \cdot 60}{60 \cdot 60} + \frac{43}{3600}$

Step 2.5.2

Multiply $60$ by $60$ .

$\frac{11 \cdot 60}{3600} + \frac{43}{3600}$

Step 2.6

Combine the numerators over the common denominator.

$\frac{11 \cdot 60 + 43}{3600}$

Step 2.7

Simplify the numerator.

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Step 2.7.1

Multiply $11$ by $60$ .

$\frac{660 + 43}{3600}$

Step 2.7.2

Add $660$ and $43$ .

$\frac{703}{3600}$

Step 3

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

$0.1952\overline{7} °$