Precalculus Examples

$\cos (\frac{317}{4})$

Step 1

Since $79$ is a whole number, it is a full degree. Since each minute is equal to $\frac{1}{60}$ degree, multiply $15$ by $\frac{1}{60}$ . Since each second is equal to $\frac{1}{3600}$ degree, multiply $0$ by $\frac{1}{3600}$ . Add them together.

$\cos (79 + 15 \cdot \frac{1}{60} + 0 \cdot \frac{1}{3600})$

Step 2

Simplify.

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Step 2.1

Remove parentheses.

$\cos (79 + 15 \cdot \frac{1}{60} + 0 \cdot \frac{1}{3600})$

Step 2.2

Simplify each term.

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Step 2.2.1

Cancel the common factor of $15$ .

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Step 2.2.1.1

Factor $15$ out of $60$ .

$\cos (79 + 15 \cdot \frac{1}{15 (4)} + 0 \cdot \frac{1}{3600})$

Step 2.2.1.2

Cancel the common factor.

$\cos (79 + 15 \cdot \frac{1}{15 \cdot 4} + 0 \cdot \frac{1}{3600})$

Step 2.2.1.3

Rewrite the expression.

$\cos (79 + \frac{1}{4} + 0 \cdot \frac{1}{3600})$

Step 2.2.2

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

$\cos (79 + \frac{1}{4} + 0)$

Step 2.3

To write $79$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\cos (79 \cdot \frac{4}{4} + \frac{1}{4} + 0)$

Step 2.4

Combine $79$ and $\frac{4}{4}$ .

$\cos (\frac{79 \cdot 4}{4} + \frac{1}{4} + 0)$

Step 2.5

Combine the numerators over the common denominator.

$\cos (\frac{79 \cdot 4 + 1}{4} + 0)$

Step 2.6

Simplify the numerator.

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Step 2.6.1

Multiply $79$ by $4$ .

$\cos (\frac{316 + 1}{4} + 0)$

Step 2.6.2

Add $316$ and $1$ .

$\cos (\frac{317}{4} + 0)$

Step 2.7

Add $\frac{317}{4}$ and $0$ .

$\cos (\frac{317}{4})$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\cos (\frac{317}{4})$

Decimal Form:

$0.18652403 \dots$