Precalculus Examples

$\csc (\frac{- 5 π}{4})$

Step 1

Move the negative in front of the fraction.

$\csc (- \frac{5 π}{4})$

Step 2

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

$\csc (\frac{3 π}{4})$

Step 3

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

$\csc (\frac{π}{4})$

Step 4

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

$\sqrt{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\sqrt{2}$

Decimal Form:

$1.41421356 \dots$