Trigonometry Examples

$0.625 (0.8 \cos (18 - (\frac{56}{30})) + 1.4 \cos (17 - (\frac{64}{30})) - 1.3025) - 0.0015$

Step 1

Simplify each term.

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Step 1.1

Simplify each term.

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Step 1.1.1

Cancel the common factor of $56$ and $30$ .

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Step 1.1.1.1

Factor $2$ out of $56$ .

$0.625 (0.8 \cos (18 - \frac{2 (28)}{30}) + 1.4 \cos (17 - (\frac{64}{30})) - 1.3025) - 0.0015$

Step 1.1.1.2

Cancel the common factors.

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Step 1.1.1.2.1

Factor $2$ out of $30$ .

$0.625 (0.8 \cos (18 - \frac{2 \cdot 28}{2 \cdot 15}) + 1.4 \cos (17 - (\frac{64}{30})) - 1.3025) - 0.0015$

Step 1.1.1.2.2

Cancel the common factor.

$0.625 (0.8 \cos (18 - \frac{2 \cdot 28}{2 \cdot 15}) + 1.4 \cos (17 - (\frac{64}{30})) - 1.3025) - 0.0015$

Step 1.1.1.2.3

Rewrite the expression.

$0.625 (0.8 \cos (18 - \frac{28}{15}) + 1.4 \cos (17 - (\frac{64}{30})) - 1.3025) - 0.0015$

Step 1.1.2

To write $18$ as a fraction with a common denominator, multiply by $\frac{15}{15}$ .

$0.625 (0.8 \cos (18 \cdot \frac{15}{15} - \frac{28}{15}) + 1.4 \cos (17 - (\frac{64}{30})) - 1.3025) - 0.0015$

Step 1.1.3

Combine $18$ and $\frac{15}{15}$ .

$0.625 (0.8 \cos (\frac{18 \cdot 15}{15} - \frac{28}{15}) + 1.4 \cos (17 - (\frac{64}{30})) - 1.3025) - 0.0015$

Step 1.1.4

Combine the numerators over the common denominator.

$0.625 (0.8 \cos (\frac{18 \cdot 15 - 28}{15}) + 1.4 \cos (17 - (\frac{64}{30})) - 1.3025) - 0.0015$

Step 1.1.5

Simplify the numerator.

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Step 1.1.5.1

Multiply $18$ by $15$ .

$0.625 (0.8 \cos (\frac{270 - 28}{15}) + 1.4 \cos (17 - (\frac{64}{30})) - 1.3025) - 0.0015$

Step 1.1.5.2

Subtract $28$ from $270$ .

$0.625 (0.8 \cos (\frac{242}{15}) + 1.4 \cos (17 - (\frac{64}{30})) - 1.3025) - 0.0015$

Step 1.1.6

Evaluate $\cos (\frac{242}{15})$ .

$0.625 (0.8 \cdot 0.96061765 + 1.4 \cos (17 - (\frac{64}{30})) - 1.3025) - 0.0015$

Step 1.1.7

Multiply $0.8$ by $0.96061765$ .

$0.625 (0.76849412 + 1.4 \cos (17 - (\frac{64}{30})) - 1.3025) - 0.0015$

Step 1.1.8

Cancel the common factor of $64$ and $30$ .

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Step 1.1.8.1

Factor $2$ out of $64$ .

$0.625 (0.76849412 + 1.4 \cos (17 - \frac{2 (32)}{30}) - 1.3025) - 0.0015$

Step 1.1.8.2

Cancel the common factors.

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Step 1.1.8.2.1

Factor $2$ out of $30$ .

$0.625 (0.76849412 + 1.4 \cos (17 - \frac{2 \cdot 32}{2 \cdot 15}) - 1.3025) - 0.0015$

Step 1.1.8.2.2

Cancel the common factor.

$0.625 (0.76849412 + 1.4 \cos (17 - \frac{2 \cdot 32}{2 \cdot 15}) - 1.3025) - 0.0015$

Step 1.1.8.2.3

Rewrite the expression.

$0.625 (0.76849412 + 1.4 \cos (17 - \frac{32}{15}) - 1.3025) - 0.0015$

Step 1.1.9

To write $17$ as a fraction with a common denominator, multiply by $\frac{15}{15}$ .

$0.625 (0.76849412 + 1.4 \cos (17 \cdot \frac{15}{15} - \frac{32}{15}) - 1.3025) - 0.0015$

Step 1.1.10

Combine $17$ and $\frac{15}{15}$ .

$0.625 (0.76849412 + 1.4 \cos (\frac{17 \cdot 15}{15} - \frac{32}{15}) - 1.3025) - 0.0015$

Step 1.1.11

Combine the numerators over the common denominator.

$0.625 (0.76849412 + 1.4 \cos (\frac{17 \cdot 15 - 32}{15}) - 1.3025) - 0.0015$

Step 1.1.12

Simplify the numerator.

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Step 1.1.12.1

Multiply $17$ by $15$ .

$0.625 (0.76849412 + 1.4 \cos (\frac{255 - 32}{15}) - 1.3025) - 0.0015$

Step 1.1.12.2

Subtract $32$ from $255$ .

$0.625 (0.76849412 + 1.4 \cos (\frac{223}{15}) - 1.3025) - 0.0015$

Step 1.1.13

Evaluate $\cos (\frac{223}{15})$ .

$0.625 (0.76849412 + 1.4 \cdot 0.9665255 - 1.3025) - 0.0015$

Step 1.1.14

Multiply $1.4$ by $0.9665255$ .

$0.625 (0.76849412 + 1.35313571 - 1.3025) - 0.0015$

Step 1.2

Add $0.76849412$ and $1.35313571$ .

$0.625 (2.12162983 - 1.3025) - 0.0015$

Step 1.3

Subtract $1.3025$ from $2.12162983$ .

$0.625 \cdot 0.81912983 - 0.0015$

Step 1.4

Multiply $0.625$ by $0.81912983$ .

$0.51195614 - 0.0015$

Step 2

Subtract $0.0015$ from $0.51195614$ .

$0.51045614$