Convert 150 degrees to radians.
Understand the Problem
The question is asking to convert an angle measurement from degrees to radians, which involves using the conversion factor that π radians is equal to 180 degrees.
Answer
\frac{5}{6} \pi radians
Answer for screen readers
The final answer is \frac{5}{6} \pi radians
Steps to Solve
- Know the conversion factor
The conversion factor between degrees and radians is that 180 degrees is equal to $\pi$ radians.
- Set up the conversion
To convert 150 degrees to radians, you can set up the following proportion:
$$ \text{radians} = 150^{\circ} \times \frac{\pi \text{ radians}}{180^{\circ}} $$
- Simplify the fraction
Perform the division inside the fraction:
$$ \text{radians} = 150 \times \frac{\pi}{180} $$ $$ \text{radians} = \frac{150}{180} \times \pi $$
- Reduce the fraction
Simplify the fraction $\frac{150}{180}$:
$$ \frac{150}{180} = \frac{5}{6} $$
- Calculate the final result
Now multiply by $\pi$:
$$ \text{radians} = \frac{5}{6} \pi $$
The final answer is \frac{5}{6} \pi radians
More Information
The conversion from degrees to radians is often necessary in mathematics, physics, and engineering, especially in trigonometry and calculus.
Tips
A common mistake is not simplifying the fraction correctly. Make sure to simplify \frac{150}{180} to \frac{5}{6} properly.
