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convert 150 to radians

Understand the Problem

The question is asking to convert an angle of 150 degrees into radians. To do this, we will use the conversion factor that π radians equals 180 degrees.

Answer

The angle of $150$ degrees is equal to $\frac{5\pi}{6}$ radians.
Answer for screen readers

The angle of $150$ degrees is equal to $\frac{5\pi}{6}$ radians.

Steps to Solve

  1. Identify the conversion factor

To convert degrees to radians, we use the fact that $180$ degrees is equal to $\pi$ radians. Therefore, the conversion formula is:

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

  1. Insert the angle in degrees into the formula

We need to convert $150$ degrees into radians. We substitute $150$ into the formula:

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

  1. Simplify the expression

Now we simplify the fraction:

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

  1. Reduce the fraction

Next, we simplify $\frac{150}{180}$. Both numbers can be divided by $30$:

$$ \frac{150 \div 30}{180 \div 30} = \frac{5}{6} $$

So, we have:

$$ \text{radians} = \frac{5\pi}{6} $$

The angle of $150$ degrees is equal to $\frac{5\pi}{6}$ radians.

More Information

Converting degrees to radians is essential in mathematics, especially in trigonometry, where angles are often expressed in radians for many calculations. The conversion factor helps in understanding the relationship between these two measurement systems.

Tips

  • Forgetting to multiply by $\frac{\pi}{180}$ instead of dividing
  • Not simplifying the fraction after calculating
  • Confusing the order of degrees and radians in calculations
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