Trigonometry Examples

$y = - 3 + 4 \cos (\frac{5 π}{6} \cdot (x + 4))$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$y = - 3 + 4 \cos (\frac{5 π}{6} x + \frac{5 π}{6} \cdot 4)$

Step 1.2

Combine $\frac{5 π}{6}$ and $x$ .

$y = - 3 + 4 \cos (\frac{5 π x}{6} + \frac{5 π}{6} \cdot 4)$

Step 1.3

Cancel the common factor of $2$ .

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Step 1.3.1

Factor $2$ out of $6$ .

$y = - 3 + 4 \cos (\frac{5 π x}{6} + \frac{5 π}{2 (3)} \cdot 4)$

Step 1.3.2

Factor $2$ out of $4$ .

$y = - 3 + 4 \cos (\frac{5 π x}{6} + \frac{5 π}{2 \cdot 3} \cdot (2 \cdot 2))$

Step 1.3.3

Cancel the common factor.

$y = - 3 + 4 \cos (\frac{5 π x}{6} + \frac{5 π}{2 \cdot 3} \cdot (2 \cdot 2))$

Step 1.3.4

Rewrite the expression.

$y = - 3 + 4 \cos (\frac{5 π x}{6} + \frac{5 π}{3} \cdot 2)$

Step 1.4

Combine $\frac{5 π}{3}$ and $2$ .

$y = - 3 + 4 \cos (\frac{5 π x}{6} + \frac{5 π \cdot 2}{3})$

Step 1.5

Multiply $2$ by $5$ .

$y = - 3 + 4 \cos (\frac{5 π x}{6} + \frac{10 π}{3})$

Step 2

A linear equation is an equation of a straight line, which means that the degree of a linear equation must be $0$ or $1$ for each of its variables. In this case, the degree of variable $y$ is $1$ , the degrees of the variables in the equation violate the linear equation definition, which means that the equation is not a linear equation.

Not Linear