Trigonometry Examples

$\sin (\arcsin (x - 9))$

Step 1

Set the argument in $\arcsin (x - 9)$ less than $- 1$ to find where the expression is undefined.

$x - 9 < - 1$

Step 2

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

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Step 2.1

Add $9$ to both sides of the inequality.

$x < - 1 + 9$

Step 2.2

Add $- 1$ and $9$ .

$x < 8$

Step 3

Set the argument in $\arcsin (x - 9)$ greater than $1$ to find where the expression is undefined.

$x - 9 > 1$

Step 4

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

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Step 4.1

Add $9$ to both sides of the inequality.

$x > 1 + 9$

Step 4.2

Add $1$ and $9$ .

$x > 10$

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 $0$ .

$x < 8, x > 10$

$(- \infty, 8) \cup (10, \infty)$

Step 6