Precalculus Examples

$\sin (\frac{3167}{60})$

Step 1

Since $52$ is a whole number, it is a full degree. Since each minute is equal to $\frac{1}{60}$ degree, multiply $47$ by $\frac{1}{60}$ . Since each second is equal to $\frac{1}{3600}$ degree, multiply $0$ by $\frac{1}{3600}$ . Add them together.

$\sin (52 + 47 \cdot \frac{1}{60} + 0 \cdot \frac{1}{3600})$

Step 2

Simplify.

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Step 2.1

Remove parentheses.

$\sin (52 + 47 \cdot \frac{1}{60} + 0 \cdot \frac{1}{3600})$

Step 2.2

Simplify each term.

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Step 2.2.1

Combine $47$ and $\frac{1}{60}$ .

$\sin (52 + \frac{47}{60} + 0 \cdot \frac{1}{3600})$

Step 2.2.2

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

$\sin (52 + \frac{47}{60} + 0)$

Step 2.3

To write $52$ as a fraction with a common denominator, multiply by $\frac{60}{60}$ .

$\sin (52 \cdot \frac{60}{60} + \frac{47}{60} + 0)$

Step 2.4

Combine $52$ and $\frac{60}{60}$ .

$\sin (\frac{52 \cdot 60}{60} + \frac{47}{60} + 0)$

Step 2.5

Combine the numerators over the common denominator.

$\sin (\frac{52 \cdot 60 + 47}{60} + 0)$

Step 2.6

Simplify the numerator.

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Step 2.6.1

Multiply $52$ by $60$ .

$\sin (\frac{3120 + 47}{60} + 0)$

Step 2.6.2

Add $3120$ and $47$ .

$\sin (\frac{3167}{60} + 0)$

Step 2.7

Add $\frac{3167}{60}$ and $0$ .

$\sin (\frac{3167}{60})$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\sin (\frac{3167}{60})$

Decimal Form:

$0.79635401 \dots$