Precalculus Examples

$arccsc (\csc (- \frac{π}{4}))$

Step 1

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

$arccsc (\csc (\frac{7 π}{4}))$

Step 2

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosecant is negative in the fourth quadrant.

$arccsc (- \csc (\frac{π}{4}))$

Step 3

The exact value of $\csc (\frac{π}{4})$ is $\sqrt{2}$ .

$arccsc (- \sqrt{2})$

Step 4

The exact value of $arccsc (- \sqrt{2})$ is $- \frac{π}{4}$ .

$- \frac{π}{4}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{π}{4}$

Decimal Form:

$- 0.78539816 \dots$