54 degrees to radians
Understand the Problem
The question is asking to convert 54 degrees into its equivalent measurement in radians. The conversion from degrees to radians can be done using the formula: radians = degrees × (π / 180).
Answer
The equivalent measurement of 54 degrees in radians is $\frac{3\pi}{10}$.
Answer for screen readers
The equivalent measurement of 54 degrees in radians is $\frac{3\pi}{10}$.
Steps to Solve
- Identify the conversion formula We know that the formula to convert degrees to radians is given by:
$$ \text{radians} = \text{degrees} \times \left( \frac{\pi}{180} \right) $$
- Plug in the values In this case, we need to convert 54 degrees to radians. We substitute 54 for degrees in the formula:
$$ \text{radians} = 54 \times \left( \frac{\pi}{180} \right) $$
- Calculate the multiplication Now, we will perform the multiplication:
$$ \text{radians} = \frac{54\pi}{180} $$
- Simplify the fraction We can simplify the fraction by finding the greatest common divisor (GCD) for 54 and 180, which is 18:
$$ \text{radians} = \frac{54 \div 18 \cdot \pi}{180 \div 18} = \frac{3\pi}{10} $$
The equivalent measurement of 54 degrees in radians is $\frac{3\pi}{10}$.
More Information
The conversion from degrees to radians is commonly used in various fields including physics and engineering, where trigonometric functions are often expressed in radians. This conversion helps in simplifying calculations involving angles and rotations.
Tips
- Failing to multiply by $\frac{\pi}{180}$ when converting degrees to radians.
- Forgetting to simplify the fraction after getting the result.
