Trigonometry Examples

$46 \cdot \frac{46 π}{180}$

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.

$(46 \cdot \frac{46 π}{180}) \cdot \frac{180 °}{π}$

Step 1.2

Cancel the common factor of $2$ .

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Step 1.2.1

Factor $2$ out of $46$ .

$2 (23) \cdot \frac{46 π}{180} \cdot \frac{180}{π}$

Step 1.2.2

Factor $2$ out of $180$ .

$2 \cdot 23 \cdot \frac{46 π}{2 \cdot 90} \cdot \frac{180}{π}$

Step 1.2.3

Cancel the common factor.

$2 \cdot 23 \cdot \frac{46 π}{2 \cdot 90} \cdot \frac{180}{π}$

Step 1.2.4

Rewrite the expression.

$23 \cdot \frac{46 π}{90} \cdot \frac{180}{π}$

Step 1.3

Combine $23$ and $\frac{46 π}{90}$ .

$\frac{23 (46 π)}{90} \cdot \frac{180}{π}$

Step 1.4

Multiply $46$ by $23$ .

$\frac{1058 π}{90} \cdot \frac{180}{π}$

Step 1.5

Cancel the common factor of $π$ .

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Step 1.5.1

Factor $π$ out of $1058 π$ .

$\frac{π \cdot 1058}{90} \cdot \frac{180}{π}$

Step 1.5.2

Cancel the common factor.

$\frac{π \cdot 1058}{90} \cdot \frac{180}{π}$

Step 1.5.3

Rewrite the expression.

$\frac{1058}{90} \cdot 180$

Step 1.6

Cancel the common factor of $90$ .

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Step 1.6.1

Factor $90$ out of $180$ .

$\frac{1058}{90} \cdot (90 (2))$

Step 1.6.2

Cancel the common factor.

$\frac{1058}{90} \cdot (90 \cdot 2)$

Step 1.6.3

Rewrite the expression.

$1058 \cdot 2$

Step 1.7

Multiply $1058$ by $2$ .

$2116$

Step 1.8

Convert to a decimal.

$2116 °$

Step 2

For angles greater than $360 °$ , subtract $360 °$ from the angle until the angle is less than $360 °$ .

$316$

Step 3

The angle is in the fourth quadrant.

Quadrant $4$

Step 4