Convert 210 degrees to radians.
Understand the Problem
The question is asking how to convert an angle of 210 degrees into radians. This involves using the formula that relates degrees to radians, which is radians = degrees × (π / 180).
Answer
The angle of 210 degrees is equal to $\frac{7\pi}{6}$ radians.
Answer for screen readers
The angle of 210 degrees is equal to $\frac{7\pi}{6}$ radians.
Steps to Solve
- Identify the conversion formula
To convert degrees to radians, we use the formula:
$$ \text{radians} = \text{degrees} \times \left( \frac{\pi}{180} \right) $$
- Plug in the angle
Now, we substitute the given angle of 210 degrees into the formula:
$$ \text{radians} = 210 \times \left( \frac{\pi}{180} \right) $$
- Simplify the calculation
Before performing the multiplication, simplify the fraction:
$$ \frac{210}{180} = \frac{21}{18} = \frac{7}{6} $$
- Calculate the final value
Now, substituting the simplified fraction back into the equation:
$$ \text{radians} = \frac{7}{6} \pi $$
So, the final value is:
$$ \text{radians} = \frac{7\pi}{6} $$
The angle of 210 degrees is equal to $\frac{7\pi}{6}$ radians.
More Information
Converting angles from degrees to radians is commonly used in mathematics, particularly in trigonometry and calculus. Radial measures provide a direct relationship to the unit circle, making them beneficial for calculations involving angles.
Tips
- Failing to simplify the fraction before multiplying.
- Misapplying the formula by not using the correct conversion factor of $\frac{\pi}{180}$.
