Trigonometry Examples

$\csc (- 30)$

Step 1

Convert the radian measure to degrees.

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Step 1.1

To convert radians to degrees, multiply by $\frac{180}{π}$ , since a full circle is $360 °$ or $2 π$ radians.

$(\csc (- 30)) \cdot \frac{180 °}{π}$

Step 1.2

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.

$- \csc (30) \cdot \frac{180}{π}$

Step 1.3

The exact value of $\csc (30)$ is $2$ .

$- 1 \cdot 2 \cdot \frac{180}{π}$

Step 1.4

Multiply $- 1$ by $2$ .

$- 2 \cdot \frac{180}{π}$

Step 1.5

Multiply $- 2 \frac{180}{π}$ .

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Step 1.5.1

Combine $- 2$ and $\frac{180}{π}$ .

$\frac{- 2 \cdot 180}{π}$

Step 1.5.2

Multiply $- 2$ by $180$ .

$\frac{- 360}{π}$

Step 1.6

Move the negative in front of the fraction.

$- \frac{360}{π}$

Step 1.7

$π$ is approximately equal to $3.14159265$ .

$- \frac{360}{3.14159265}$

Step 1.8

Convert to a decimal.

$- 114.59155902 °$

Step 2

For angles smaller than $0 °$ , add $360 °$ to the angle until the angle is larger than $0 °$ .

$245.40844097$

Step 3

The angle is in the third quadrant.

Quadrant $3$

Step 4