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

  1. Know the conversion factor

The conversion factor between degrees and radians is that 180 degrees is equal to $\pi$ radians.

  1. Set up the conversion

To convert 150 degrees to radians, you can set up the following proportion:

$$ \text{radians} = 150^{\circ} \times \frac{\pi \text{ radians}}{180^{\circ}} $$

  1. Simplify the fraction

Perform the division inside the fraction:

$$ \text{radians} = 150 \times \frac{\pi}{180} $$ $$ \text{radians} = \frac{150}{180} \times \pi $$

  1. Reduce the fraction

Simplify the fraction $\frac{150}{180}$:

$$ \frac{150}{180} = \frac{5}{6} $$

  1. 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.

Thank you for voting!
Use Quizgecko on...
Browser
Browser