Trigonometry Examples

$\arctan (\frac{1}{\arccos (u)})$

Step 1

Set the denominator in $\frac{1}{\arccos (u)}$ equal to $0$ to find where the expression is undefined.

$\arccos (u) = 0$

Step 2

Solve for $u$ .

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Step 2.1

Take the inverse arccosine of both sides of the equation to extract $u$ from inside the arccosine.

$u = \cos (0)$

Step 2.2

Simplify the right side.

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Step 2.2.1

The exact value of $\cos (0)$ is $1$ .

$u = 1$

Step 3

Set the argument in $\arccos (u)$ less than $- 1$ to find where the expression is undefined.

$u < - 1$

Step 4

Set the argument in $\arccos (u)$ greater than $1$ to find where the expression is undefined.

$u > 1$

Step 5

The equation is undefined where the denominator equals $0$ , the argument of a square root is less than $0$ , or the argument of a logarithm is less than or equal to $0$ .

$u < - 1, u \geq 1$

$(- \infty, - 1) \cup [1, \infty)$

Step 6