Algebra Examples

$100 \cos (θ) = w (\frac{5}{13})$

Step 1

Combine $w$ and $\frac{5}{13}$ .

$100 \cos (θ) = \frac{w \cdot 5}{13}$

Step 2

Divide each term in $100 \cos (θ) = \frac{w \cdot 5}{13}$ by $100$ and simplify.

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Step 2.1

Divide each term in $100 \cos (θ) = \frac{w \cdot 5}{13}$ by $100$ .

$\frac{100 \cos (θ)}{100} = \frac{\frac{w \cdot 5}{13}}{100}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $100$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{100 \cos (θ)}{100} = \frac{\frac{w \cdot 5}{13}}{100}$

Step 2.2.1.2

Divide $\cos (θ)$ by $1$ .

$\cos (θ) = \frac{\frac{w \cdot 5}{13}}{100}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply the numerator by the reciprocal of the denominator.

$\cos (θ) = \frac{w \cdot 5}{13} \cdot \frac{1}{100}$

Step 2.3.2

Cancel the common factor of $5$ .

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Step 2.3.2.1

Factor $5$ out of $w \cdot 5$ .

$\cos (θ) = \frac{5 \cdot w}{13} \cdot \frac{1}{100}$

Step 2.3.2.2

Factor $5$ out of $100$ .

$\cos (θ) = \frac{5 \cdot w}{13} \cdot \frac{1}{5 (20)}$

Step 2.3.2.3

Cancel the common factor.

$\cos (θ) = \frac{5 \cdot w}{13} \cdot \frac{1}{5 \cdot 20}$

Step 2.3.2.4

Rewrite the expression.

$\cos (θ) = \frac{w}{13} \cdot \frac{1}{20}$

Step 2.3.3

Multiply $\frac{w}{13}$ by $\frac{1}{20}$ .

$\cos (θ) = \frac{w}{13 \cdot 20}$

Step 2.3.4

Multiply $13$ by $20$ .

$\cos (θ) = \frac{w}{260}$

Step 3

Take the inverse cosine of both sides of the equation to extract $θ$ from inside the cosine.

$θ = \arccos (\frac{w}{260})$