Trigonometry Examples

$4 + \frac{23}{60}$

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.

$(4 + \frac{23}{60}) \cdot \frac{180 °}{π}$

Step 1.2

To write $4$ as a fraction with a common denominator, multiply by $\frac{60}{60}$ .

$(4 \cdot \frac{60}{60} + \frac{23}{60}) \cdot \frac{180}{π}$

Step 1.3

Combine $4$ and $\frac{60}{60}$ .

$(\frac{4 \cdot 60}{60} + \frac{23}{60}) \cdot \frac{180}{π}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{4 \cdot 60 + 23}{60} \cdot \frac{180}{π}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $4$ by $60$ .

$\frac{240 + 23}{60} \cdot \frac{180}{π}$

Step 1.5.2

Add $240$ and $23$ .

$\frac{263}{60} \cdot \frac{180}{π}$

Step 1.6

Cancel the common factor of $60$ .

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Step 1.6.1

Factor $60$ out of $180$ .

$\frac{263}{60} \cdot \frac{60 (3)}{π}$

Step 1.6.2

Cancel the common factor.

$\frac{263}{60} \cdot \frac{60 \cdot 3}{π}$

Step 1.6.3

Rewrite the expression.

$263 \cdot \frac{3}{π}$

Step 1.7

Combine $263$ and $\frac{3}{π}$ .

$\frac{263 \cdot 3}{π}$

Step 1.8

Multiply $263$ by $3$ .

$\frac{789}{π}$

Step 1.9

$π$ is approximately equal to $3.14159265$ .

$\frac{789}{3.14159265}$

Step 1.10

Convert to a decimal.

$251.14650019 °$

Step 2

The angle is in the third quadrant.

Quadrant $3$

Step 3