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
- 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:
$$ \text{radians} = \text{degrees} \times \frac{\pi}{180} $$
- Insert the angle in degrees into the formula
We need to convert $150$ degrees into radians. We substitute $150$ into the formula:
$$ \text{radians} = 150 \times \frac{\pi}{180} $$
- Simplify the expression
Now we simplify the fraction:
$$ \text{radians} = 150 \times \frac{\pi}{180} = \frac{150\pi}{180} $$
- 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
