Trigonometry Examples

$- \frac{1 π}{4}$

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.

$(- \frac{1 π}{4}) \cdot \frac{180 °}{π}$

Step 1.2

Multiply $π$ by $1$ .

$- \frac{π}{4} \cdot \frac{180}{π}$

Step 1.3

Cancel the common factor of $π$ .

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Step 1.3.1

Move the leading negative in $- \frac{π}{4}$ into the numerator.

$\frac{- π}{4} \cdot \frac{180}{π}$

Step 1.3.2

Factor $π$ out of $- π$ .

$\frac{π \cdot - 1}{4} \cdot \frac{180}{π}$

Step 1.3.3

Cancel the common factor.

$\frac{π \cdot - 1}{4} \cdot \frac{180}{π}$

Step 1.3.4

Rewrite the expression.

$\frac{- 1}{4} \cdot 180$

Step 1.4

Cancel the common factor of $4$ .

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Step 1.4.1

Factor $4$ out of $180$ .

$\frac{- 1}{4} \cdot (4 (45))$

Step 1.4.2

Cancel the common factor.

$\frac{- 1}{4} \cdot (4 \cdot 45)$

Step 1.4.3

Rewrite the expression.

$- 1 \cdot 45$

Step 1.5

Multiply $- 1$ by $45$ .

$- 45$

Step 1.6

Convert to a decimal.

$- 45 °$

Step 2

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

$315$

Step 3

The angle is in the fourth quadrant.

Quadrant $4$

Step 4