Trigonometry Examples

$\frac{45}{24}$

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.

$(\frac{45}{24}) \cdot \frac{180 °}{π}$

Step 1.2

Cancel the common factor of $12$ .

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Step 1.2.1

Factor $12$ out of $24$ .

$\frac{45}{12 (2)} \cdot \frac{180}{π}$

Step 1.2.2

Factor $12$ out of $180$ .

$\frac{45}{12 \cdot 2} \cdot \frac{12 \cdot 15}{π}$

Step 1.2.3

Cancel the common factor.

$\frac{45}{12 \cdot 2} \cdot \frac{12 \cdot 15}{π}$

Step 1.2.4

Rewrite the expression.

$\frac{45}{2} \cdot \frac{15}{π}$

Step 1.3

Multiply $\frac{45}{2}$ by $\frac{15}{π}$ .

$\frac{45 \cdot 15}{2 π}$

Step 1.4

Multiply $45$ by $15$ .

$\frac{675}{2 π}$

Step 1.5

Cancel the common factor of $675$ and $2$ .

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Step 1.5.1

Rewrite $675$ as $1 (675)$ .

$\frac{1 (675)}{2 π}$

Step 1.5.2

Cancel the common factors.

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Step 1.5.2.1

Factor $1$ out of $2 π$ .

$\frac{1 (675)}{1 (2 π)}$

Step 1.5.2.2

Cancel the common factor.

$\frac{1 \cdot 675}{1 (2 π)}$

Step 1.5.2.3

Rewrite the expression.

$\frac{675}{2 π}$

Step 1.6

$π$ is approximately equal to $3.14159265$ .

$\frac{675}{2 (3.14159265)}$

Step 1.7

Convert to a decimal.

$107.42958658 °$

Step 2

The angle is in the second quadrant.

Quadrant $2$

Step 3