Trigonometry Examples

$4 π + 4 \arctan (x) = π$

Step 1

Move all terms not containing $x$ to the right side of the equation.

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Step 1.1

Subtract $4 π$ from both sides of the equation.

$4 \arctan (x) = π - 4 π$

Step 1.2

Subtract $4 π$ from $π$ .

$4 \arctan (x) = - 3 π$

Step 2

Divide each term in $4 \arctan (x) = - 3 π$ by $4$ and simplify.

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Step 2.1

Divide each term in $4 \arctan (x) = - 3 π$ by $4$ .

$\frac{4 \arctan (x)}{4} = \frac{- 3 π}{4}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $4$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{4 \arctan (x)}{4} = \frac{- 3 π}{4}$

Step 2.2.1.2

Divide $\arctan (x)$ by $1$ .

$\arctan (x) = \frac{- 3 π}{4}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Move the negative in front of the fraction.

$\arctan (x) = - \frac{3 π}{4}$

Step 3

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

$x = \tan (- \frac{3 π}{4})$

Step 4

Simplify the right side.

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Step 4.1

Simplify $\tan (- \frac{3 π}{4})$ .

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Step 4.1.1

Add full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$x = \tan (\frac{5 π}{4})$

Step 4.1.2

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

$x = \tan (\frac{π}{4})$

Step 4.1.3

The exact value of $\tan (\frac{π}{4})$ is $1$ .

$x = 1$

Step 5

Exclude the solutions that do not make $4 π + 4 \arctan (x) = π$ true.

$No solution$