Trigonometry Examples

$\csc (- \frac{3}{4} \cdot π)$

Step 1

Combine $π$ and $\frac{3}{4}$ .

$\csc (- \frac{π \cdot 3}{4})$

Step 2

Move $3$ to the left of $π$ .

$\csc (- \frac{3 \cdot π}{4})$

Step 3

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

$\csc (\frac{5 π}{4})$

Step 4

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.

$- \csc (\frac{π}{4})$

Step 5

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

$- \sqrt{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \sqrt{2}$

Decimal Form:

$- 1.41421356 \dots$