Trigonometry Examples

$\frac{5 π}{8}$

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.

$(\frac{5 π}{8}) \cdot \frac{180 °}{π}$

Step 1.2

Cancel the common factor of $π$ .

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Step 1.2.1

Factor $π$ out of $5 π$ .

$\frac{π \cdot 5}{8} \cdot \frac{180}{π}$

Step 1.2.2

Cancel the common factor.

$\frac{π \cdot 5}{8} \cdot \frac{180}{π}$

Step 1.2.3

Rewrite the expression.

$\frac{5}{8} \cdot 180$

Step 1.3

Cancel the common factor of $4$ .

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Step 1.3.1

Factor $4$ out of $8$ .

$\frac{5}{4 (2)} \cdot 180$

Step 1.3.2

Factor $4$ out of $180$ .

$\frac{5}{4 \cdot 2} \cdot (4 \cdot 45)$

Step 1.3.3

Cancel the common factor.

$\frac{5}{4 \cdot 2} \cdot (4 \cdot 45)$

Step 1.3.4

Rewrite the expression.

$\frac{5}{2} \cdot 45$

Step 1.4

Combine $\frac{5}{2}$ and $45$ .

$\frac{5 \cdot 45}{2}$

Step 1.5

Multiply $5$ by $45$ .

$\frac{225}{2}$

Step 1.6

Convert to a decimal.

$112.5 °$

Step 2

The angle is in the second quadrant.

Quadrant $2$

Step 3