Trigonometry Examples

$y = 5 \cos^{- 4} (x) + \sin (x) \cos (x)$

Step 1

Simplify each term.

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Step 1.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$y = 5 \frac{1}{\cos^{4} (x)} + \sin (x) \cos (x)$

Step 1.2

Combine $5$ and $\frac{1}{\cos^{4} (x)}$ .

$y = \frac{5}{\cos^{4} (x)} + \sin (x) \cos (x)$

Step 1.3

Multiply by $1$ .

$y = \frac{5}{\cos^{4} (x) \cdot 1} + \sin (x) \cos (x)$

Step 1.4

Separate fractions.

$y = \frac{5}{1} \cdot \frac{1}{\cos^{4} (x)} + \sin (x) \cos (x)$

Step 1.5

Convert from $\frac{1}{\cos^{4} (x)}$ to $\sec^{4} (x)$ .

$y = \frac{5}{1} \sec^{4} (x) + \sin (x) \cos (x)$

Step 1.6

Divide $5$ by $1$ .

$y = 5 \sec^{4} (x) + \sin (x) \cos (x)$

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