Find the Quadrant of the Angle (7pi)/4

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Trigonometry

$\frac{7 π}{4}$

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.

$(\frac{7 π}{4}) \cdot \frac{180 °}{π}$

Cancel the common factor of $π$ .

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Factor $π$ out of $7 π$ .

$\frac{π \cdot 7}{4} \cdot \frac{180}{π}$

Cancel the common factor.

$\frac{π \cdot 7}{4} \cdot \frac{180}{π}$

Rewrite the expression.

$\frac{7}{4} \cdot 180$

Cancel the common factor of $4$ .

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Factor $4$ out of $180$ .

$\frac{7}{4} \cdot (4 (45))$

Cancel the common factor.

$\frac{7}{4} \cdot (4 \cdot 45)$

Rewrite the expression.

$7 \cdot 45$

Multiply $7$ by $45$ .

$315$

Convert to a decimal.

$315 °$

The angle is in the fourth quadrant.

Quadrant $4$

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