Trigonometry Examples

$x \arctan (x) = x$ , $(0, 2)$

Step 1

Subtract $x$ from both sides of the equation.

$x \arctan (x) - x = 0$

Step 2

Factor $x$ out of $x \arctan (x) - x$ .

Tap for more steps...

Step 2.1

Factor $x$ out of $x \arctan (x)$ .

$x (\arctan (x)) - x = 0$

Step 2.2

Factor $x$ out of $- x$ .

$x (\arctan (x)) + x \cdot - 1 = 0$

Step 2.3

Factor $x$ out of $x (\arctan (x)) + x \cdot - 1$ .

$x (\arctan (x) - 1) = 0$

Step 3

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x = 0$

$\arctan (x) - 1 = 0$

Step 4

Set $x$ equal to $0$ .

$x = 0$

Step 5

Set $\arctan (x) - 1$ equal to $0$ and solve for $x$ .

Tap for more steps...

Step 5.1

Set $\arctan (x) - 1$ equal to $0$ .

$\arctan (x) - 1 = 0$

Step 5.2

Solve $\arctan (x) - 1 = 0$ for $x$ .

Tap for more steps...

Step 5.2.1

Add $1$ to both sides of the equation.

$\arctan (x) = 1$

Step 5.2.2

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

$x = \tan (1)$

Step 5.2.3

Simplify the right side.

Tap for more steps...

Step 5.2.3.1

Evaluate $\tan (1)$ .

$x = 0.01745506$

Step 6

The final solution is all the values that make $x (\arctan (x) - 1) = 0$ true.

$x = 0, 0.01745506$

Step 7

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

$x = 0$

Step 8

No values of $x$ fall on the interval $(0, 2)$ . The equation has no solution over the interval.

No solution