Trigonometry Examples

$\arctan (\tan (x)) = \arctan (\frac{y}{x})$

Step 1

Solve the equation for $y$ .

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Step 1.1

Rewrite the equation as $\arctan (\frac{y}{x}) = \arctan (\tan (x))$ .

$\arctan (\frac{y}{x}) = \arctan (\tan (x))$

Step 1.2

Take the inverse arctangent of both sides of the equation to extract $y$ from inside the arctangent.

$\frac{y}{x} = \tan (\arctan (\tan (x)))$

Step 1.3

Simplify the right side.

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Step 1.3.1

The functions tangent and arctangent are inverses.

$\frac{y}{x} = \tan (x)$

Step 1.4

Multiply both sides by $x$ .

$\frac{y}{x} x = \tan (x) x$

Step 1.5

Simplify.

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Step 1.5.1

Simplify the left side.

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Step 1.5.1.1

Cancel the common factor of $x$ .

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Step 1.5.1.1.1

Cancel the common factor.

$\frac{y}{x} x = \tan (x) x$

Step 1.5.1.1.2

Rewrite the expression.

$y = \tan (x) x$

Step 1.5.2

Simplify the right side.

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Step 1.5.2.1

Reorder factors in $\tan (x) x$ .

$y = x \tan (x)$

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