Trigonometry Examples

$f (x) = \frac{y}{2} \cdot f (x)$

Step 1

Rewrite the function as an equation.

$y = \frac{y}{2} \cdot f (x)$

Step 2

Combine $\frac{y}{2}$ and $f (x)$ .

$y = \frac{y f (x)}{2}$

Step 3

Subtract $\frac{y f (x)}{2}$ from both sides of the equation.

$y - \frac{y f (x)}{2} = 0$

Step 4

Multiply $y f$ by $x$ .

$y - \frac{y f x}{2} = 0$

Step 5

Factor $y$ out of $y - \frac{y f x}{2}$ .

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Step 5.1

Factor $y$ out of $y^{1}$ .

$y \cdot 1 - \frac{y f x}{2} = 0$

Step 5.2

Factor $y$ out of $- \frac{y f x}{2}$ .

$y \cdot 1 + y (- \frac{f x}{2}) = 0$

Step 5.3

Factor $y$ out of $y \cdot 1 + y (- \frac{f x}{2})$ .

$y (1 - \frac{f x}{2}) = 0$

Step 6

Divide each term in $y (1 - \frac{f x}{2}) = 0$ by $1 - \frac{f x}{2}$ and simplify.

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Step 6.1

Divide each term in $y (1 - \frac{f x}{2}) = 0$ by $1 - \frac{f x}{2}$ .

$\frac{y (1 - \frac{f x}{2})}{1 - \frac{f x}{2}} = \frac{0}{1 - \frac{f x}{2}}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $1 - \frac{f x}{2}$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{y (1 - \frac{f x}{2})}{1 - \frac{f x}{2}} = \frac{0}{1 - \frac{f x}{2}}$

Step 6.2.1.2

Divide $y$ by $1$ .

$y = \frac{0}{1 - \frac{f x}{2}}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Simplify the denominator.

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Step 6.3.1.1

Write $1$ as a fraction with a common denominator.

$y = \frac{0}{\frac{2}{2} - \frac{f x}{2}}$

Step 6.3.1.2

Combine the numerators over the common denominator.

$y = \frac{0}{\frac{2 - f x}{2}}$

Step 6.3.2

Multiply the numerator by the reciprocal of the denominator.

$y = 0 \frac{2}{2 - f x}$

Step 6.3.3

Multiply $0$ by $\frac{2}{2 - f x}$ .

$y = 0$

Step 7

Use the slope-intercept form to find the slope and y-intercept.

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Step 7.1

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Step 7.2

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m = 0$

$b = 0$

Step 7.3

The slope of the line is the value of $m$ , and the y-intercept is the value of $b$ .

Slope: $0$

y-intercept: $(0, 0)$

Slope: $0$

y-intercept: $(0, 0)$

Step 8