Trigonometry Examples

$\csc (495)$

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.

$(\csc (495)) \cdot \frac{180 °}{π}$

Step 1.2

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

$\csc (135) \cdot \frac{180}{π}$

Step 1.3

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

$\csc (45) \cdot \frac{180}{π}$

Step 1.4

The exact value of $\csc (45)$ is $\sqrt{2}$ .

$\sqrt{2} \cdot \frac{180}{π}$

Step 1.5

Combine $\sqrt{2}$ and $\frac{180}{π}$ .

$\frac{\sqrt{2} \cdot 180}{π}$

Step 1.6

Move $180$ to the left of $\sqrt{2}$ .

$\frac{180 \sqrt{2}}{π}$

Step 1.7

$π$ is approximately equal to $3.14159265$ .

$\frac{180 \sqrt{2}}{3.14159265}$

Step 1.8

Convert to a decimal.

$81.02846845 °$

Step 2

The angle is in the first quadrant.

Quadrant $1$

Step 3