Trigonometry Examples

$\csc (390)$

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.

$(\csc (390)) \cdot \frac{180 °}{π}$

Step 1.2

Remove full rotations of $360$ ° until the angle is between $0$ ° and $360$ °.

$\csc (30) \cdot \frac{180}{π}$

Step 1.3

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

$2 \cdot \frac{180}{π}$

Step 1.4

Multiply $2 \frac{180}{π}$ .

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Step 1.4.1

Combine $2$ and $\frac{180}{π}$ .

$\frac{2 \cdot 180}{π}$

Step 1.4.2

Multiply $2$ by $180$ .

$\frac{360}{π}$

Step 1.5

$π$ is approximately equal to $3.14159265$ .

$\frac{360}{3.14159265}$

Step 1.6

Convert to a decimal.

$114.59155902 °$

Step 2

The angle is in the second quadrant.

Quadrant $2$

Step 3