Convert 18 degrees to radians.
Understand the Problem
The question is asking to convert an angle given in degrees, specifically 18 degrees, into radians. The conversion from degrees to radians can be done using the formula: radians = degrees × (π / 180).
Answer
The angle of 18 degrees is equivalent to $\frac{\pi}{10}$ radians.
Answer for screen readers
The angle of 18 degrees is equivalent to $\frac{\pi}{10}$ radians.
Steps to Solve
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Start with the degree measurement We have the angle given in degrees, which is 18 degrees.
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Write the conversion formula To convert degrees to radians, we use the formula:
$$ \text{radians} = \text{degrees} \times \left( \frac{\pi}{180} \right) $$ -
Substitute the degree value into the formula Now we substitute the value of degrees into the formula:
$$ \text{radians} = 18 \times \left( \frac{\pi}{180} \right) $$ -
Simplify the expression We can simplify the expression by dividing 18 by 180:
$$ \frac{18}{180} = \frac{1}{10} $$
So,
$$ \text{radians} = \frac{1}{10} \pi $$ -
Write the final answer The final expression for the angle in radians is:
$$ \text{radians} = \frac{\pi}{10} $$
The angle of 18 degrees is equivalent to $\frac{\pi}{10}$ radians.
More Information
Converting between degrees and radians is important in mathematics, especially in trigonometry and calculus, as different applications may use one system over the other. Notably, $180$ degrees is equal to $\pi$ radians, which helps visualize the relationship.
Tips
- Not using the correct conversion factor: Some may forget to multiply by $\frac{\pi}{180}$. Ensure to always include this factor.
- Not simplifying properly: When simplifying fractions, remember to reduce them to the lowest terms.
