Finite Math Examples

$\frac{x}{a} \cdot \cos (a) + \frac{y}{b} \cdot \sin (a) = 1$

Step 1

Simplify the left side.

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $\frac{x}{a}$ and $\cos (a)$ .

$\frac{x \cos (a)}{a} + \frac{y}{b} \cdot \sin (a) = 1$

Step 1.1.2

Combine $\frac{y}{b}$ and $\sin (a)$ .

$\frac{x \cos (a)}{a} + \frac{y \sin (a)}{b} = 1$

Step 2

Subtract $\frac{y \sin (a)}{b}$ from both sides of the equation.

$\frac{x \cos (a)}{a} = 1 - \frac{y \sin (a)}{b}$

Step 3

Multiply both sides by $a$ .

$\frac{x \cos (a)}{a} a = (1 - \frac{y \sin (a)}{b}) a$

Step 4

Simplify.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Cancel the common factor of $a$ .

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Step 4.1.1.1

Cancel the common factor.

$\frac{x \cos (a)}{a} a = (1 - \frac{y \sin (a)}{b}) a$

Step 4.1.1.2

Rewrite the expression.

$x \cos (a) = (1 - \frac{y \sin (a)}{b}) a$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $(1 - \frac{y \sin (a)}{b}) a$ .

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Step 4.2.1.1

Apply the distributive property.

$x \cos (a) = 1 a - \frac{y \sin (a)}{b} a$

Step 4.2.1.2

Multiply $a$ by $1$ .

$x \cos (a) = a - \frac{y \sin (a)}{b} a$

Step 4.2.1.3

Combine $a$ and $\frac{y \sin (a)}{b}$ .

$x \cos (a) = a - \frac{a y \sin (a)}{b}$

Step 5

Divide each term in $x \cos (a) = a - \frac{a y \sin (a)}{b}$ by $\cos (a)$ and simplify.

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Step 5.1

Divide each term in $x \cos (a) = a - \frac{a y \sin (a)}{b}$ by $\cos (a)$ .

$\frac{x \cos (a)}{\cos (a)} = \frac{a}{\cos (a)} + \frac{- \frac{a y \sin (a)}{b}}{\cos (a)}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $\cos (a)$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{x \cos (a)}{\cos (a)} = \frac{a}{\cos (a)} + \frac{- \frac{a y \sin (a)}{b}}{\cos (a)}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{a}{\cos (a)} + \frac{- \frac{a y \sin (a)}{b}}{\cos (a)}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Simplify each term.

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Step 5.3.1.1

Separate fractions.

$x = \frac{a}{1} \cdot \frac{1}{\cos (a)} + \frac{- \frac{a y \sin (a)}{b}}{\cos (a)}$

Step 5.3.1.2

Convert from $\frac{1}{\cos (a)}$ to $\sec (a)$ .

$x = \frac{a}{1} \sec (a) + \frac{- \frac{a y \sin (a)}{b}}{\cos (a)}$

Step 5.3.1.3

Divide $a$ by $1$ .

$x = a \sec (a) + \frac{- \frac{a y \sin (a)}{b}}{\cos (a)}$

Step 5.3.1.4

Multiply the numerator by the reciprocal of the denominator.

$x = a \sec (a) - \frac{a y \sin (a)}{b} \cdot \frac{1}{\cos (a)}$

Step 5.3.1.5

Convert from $\frac{1}{\cos (a)}$ to $\sec (a)$ .

$x = a \sec (a) - \frac{a y \sin (a)}{b} \sec (a)$

Step 5.3.1.6

Combine $\sec (a)$ and $\frac{a y \sin (a)}{b}$ .

$x = a \sec (a) - \frac{\sec (a) (a y \sin (a))}{b}$

Step 5.3.1.7

Remove unnecessary parentheses.

$x = a \sec (a) - \frac{\sec (a) a y \sin (a)}{b}$

Step 5.3.2

Reorder factors in $a \sec (a) - \frac{\sec (a) a y \sin (a)}{b}$ .

$x = a \sec (a) - \frac{a y \sec (a) \sin (a)}{b}$