Find the Quadrant of the Angle -(29pi)/6

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Trigonometry

$- \frac{29 π}{6}$

Convert the radian measure to degrees.

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

$(- \frac{29 π}{6}) \cdot \frac{180 °}{π}$

Cancel the common factor of $π$ .

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Move the leading negative in $- \frac{29 π}{6}$ into the numerator.

$\frac{- 29 π}{6} \cdot \frac{180}{π}$

Factor $π$ out of $- 29 π$ .

$\frac{π \cdot - 29}{6} \cdot \frac{180}{π}$

Cancel the common factor.

$\frac{π \cdot - 29}{6} \cdot \frac{180}{π}$

Rewrite the expression.

$\frac{- 29}{6} \cdot 180$

Cancel the common factor of $6$ .

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Factor $6$ out of $180$ .

$\frac{- 29}{6} \cdot (6 (30))$

Cancel the common factor.

$\frac{- 29}{6} \cdot (6 \cdot 30)$

Rewrite the expression.

$- 29 \cdot 30$

Multiply $- 29$ by $30$ .

$- 870$

Convert to a decimal.

$- 870 °$

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

$210$

The angle is in the third quadrant.

Quadrant $3$

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