Trigonometry Examples

$y = \cot (4 x) + 1$

Step 1

Rewrite the equation as $\cot (4 x) + 1 = y$ .

$\cot (4 x) + 1 = y$

Step 2

Subtract $1$ from both sides of the equation.

$\cot (4 x) = y - 1$

Step 3

Take the inverse cotangent of both sides of the equation to extract $x$ from inside the cotangent.

$4 x = arccot (y - 1)$

Step 4

Divide each term in $4 x = arccot (y - 1)$ by $4$ and simplify.

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Step 4.1

Divide each term in $4 x = arccot (y - 1)$ by $4$ .

$\frac{4 x}{4} = \frac{arccot (y - 1)}{4}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $4$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{arccot (y - 1)}{4}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{arccot (y - 1)}{4}$