Trigonometry Examples

$\csc (210)$

Step 1

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

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.

$- \csc (30) \cdot \frac{π}{180}$ radians

Step 3

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

$- 1 \cdot 2 \cdot \frac{π}{180}$ radians

Step 4

Cancel the common factor of $2$ .

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Step 4.1

Factor $2$ out of $- 1 \cdot 2$ .

$2 \cdot - 1 \cdot \frac{π}{180}$ radians

Step 4.2

Factor $2$ out of $180$ .

$2 \cdot - 1 \cdot \frac{π}{2 (90)}$ radians

Step 4.3

Cancel the common factor.

$2 \cdot - 1 \cdot \frac{π}{2 \cdot 90}$ radians

Step 4.4

Rewrite the expression.

$- 1 \cdot \frac{π}{90}$ radians

Step 5

Rewrite $- 1 \frac{π}{90}$ as $- \frac{π}{90}$ .

$- \frac{π}{90}$ radians