Trigonometry Examples

$\frac{28}{40}$

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.

$(\frac{28}{40}) \cdot \frac{180 °}{π}$

Step 1.2

Cancel the common factor of $20$ .

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Step 1.2.1

Factor $20$ out of $40$ .

$\frac{28}{20 (2)} \cdot \frac{180}{π}$

Step 1.2.2

Factor $20$ out of $180$ .

$\frac{28}{20 \cdot 2} \cdot \frac{20 \cdot 9}{π}$

Step 1.2.3

Cancel the common factor.

$\frac{28}{20 \cdot 2} \cdot \frac{20 \cdot 9}{π}$

Step 1.2.4

Rewrite the expression.

$\frac{28}{2} \cdot \frac{9}{π}$

Step 1.3

Multiply $\frac{28}{2}$ by $\frac{9}{π}$ .

$\frac{28 \cdot 9}{2 π}$

Step 1.4

Multiply $28$ by $9$ .

$\frac{252}{2 π}$

Step 1.5

Cancel the common factor of $252$ and $2$ .

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Step 1.5.1

Factor $2$ out of $252$ .

$\frac{2 \cdot 126}{2 π}$

Step 1.5.2

Cancel the common factors.

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Step 1.5.2.1

Factor $2$ out of $2 π$ .

$\frac{2 \cdot 126}{2 (π)}$

Step 1.5.2.2

Cancel the common factor.

$\frac{2 \cdot 126}{2 π}$

Step 1.5.2.3

Rewrite the expression.

$\frac{126}{π}$

Step 1.6

$π$ is approximately equal to $3.14159265$ .

$\frac{126}{3.14159265}$

Step 1.7

Convert to a decimal.

$40.10704565 °$

Step 2

The angle is in the first quadrant.

Quadrant $1$

Step 3