Trigonometry Examples

$- \frac{π}{150}$

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.

$(- \frac{π}{150}) \cdot \frac{180 °}{π}$

Step 1.2

Cancel the common factor of $π$ .

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Step 1.2.1

Move the leading negative in $- \frac{π}{150}$ into the numerator.

$\frac{- π}{150} \cdot \frac{180}{π}$

Step 1.2.2

Factor $π$ out of $- π$ .

$\frac{π \cdot - 1}{150} \cdot \frac{180}{π}$

Step 1.2.3

Cancel the common factor.

$\frac{π \cdot - 1}{150} \cdot \frac{180}{π}$

Step 1.2.4

Rewrite the expression.

$\frac{- 1}{150} \cdot 180$

Step 1.3

Cancel the common factor of $30$ .

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Step 1.3.1

Factor $30$ out of $150$ .

$\frac{- 1}{30 (5)} \cdot 180$

Step 1.3.2

Factor $30$ out of $180$ .

$\frac{- 1}{30 \cdot 5} \cdot (30 \cdot 6)$

Step 1.3.3

Cancel the common factor.

$\frac{- 1}{30 \cdot 5} \cdot (30 \cdot 6)$

Step 1.3.4

Rewrite the expression.

$\frac{- 1}{5} \cdot 6$

Step 1.4

Combine $\frac{- 1}{5}$ and $6$ .

$\frac{- 1 \cdot 6}{5}$

Step 1.5

Simplify the expression.

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Step 1.5.1

Multiply $- 1$ by $6$ .

$\frac{- 6}{5}$

Step 1.5.2

Move the negative in front of the fraction.

$- \frac{6}{5}$

Step 1.6

Convert to a decimal.

$- 1.2 °$

Step 2

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

$358.8$

Step 3

The angle is in the fourth quadrant.

Quadrant $4$

Step 4