Precalculus Examples

$\csc (\frac{31 π}{6})$

Step 1

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

$\csc (\frac{7 π}{6})$

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 third quadrant.

$- \csc (\frac{π}{6})$

Step 3

The exact value of $\csc (\frac{π}{6})$ is $2$ .

$- 1 \cdot 2$

Step 4

Multiply $- 1$ by $2$ .

$- 2$