Convert 150 degrees to radians.
Understand the Problem
The question is asking how to convert an angle measured in degrees (150 degrees) into radians. The conversion can be done by using the formula: radians = degrees × (π / 180).
Answer
The angle $150$ degrees is equal to $\frac{5\pi}{6}$ radians.
Answer for screen readers
The angle $150$ degrees is equal to $\frac{5\pi}{6}$ radians.
Steps to Solve
- Identify the angle in degrees
The angle given in the problem is $150$ degrees.
- Set up 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 $150$ degrees into the formula:
$$ \text{radians} = 150 \times \left( \frac{\pi}{180} \right) $$
- Simplify the expression
Calculate the multiplication:
$$ \text{radians} = \frac{150\pi}{180} $$
- Reduce the fraction
Now we need to simplify $\frac{150\pi}{180}$. We can divide both the numerator and the denominator by $30$:
$$ \text{radians} = \frac{150 \div 30}{180 \div 30} \pi = \frac{5\pi}{6} $$
The angle $150$ degrees is equal to $\frac{5\pi}{6}$ radians.
More Information
Converting degrees to radians is essential in many fields, such as physics and engineering, particularly when working with circular motion and angular measurements. The formula helps establish a direct relationship between the two measurement systems.
Tips
- Forgetting to multiply by $\frac{\pi}{180}$, resulting in not converting degrees to radians properly.
- Not simplifying the fraction at the end, leading to an incorrect or complex answer.
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