Convert 110 degrees to radians using the ratio \frac{?}{180}
The Correct Answer and Explanation is:
To convert degrees to radians, you can use the following formula: radians=degrees×π180\text{radians} = \text{degrees} \times \frac{\pi}{180}radians=degrees×180π
In this case, to convert 110 degrees to radians: 110 degrees×π180110 \, \text{degrees} \times \frac{\pi}{180}110degrees×180π
Now, simplify the multiplication: 110×π180=110π180110 \times \frac{\pi}{180} = \frac{110\pi}{180}110×180π=180110π
We can simplify the fraction 110180\frac{110}{180}180110 by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 10: 110180=1118\frac{110}{180} = \frac{11}{18}180110=1811
So, the equation becomes: 11π18\frac{11\pi}{18}1811π
Thus, 110 degrees is equivalent to: 11π18 radians\frac{11\pi}{18} \, \text{radians}1811πradians
Explanation:
- Degrees to Radians Conversion: The relationship between degrees and radians is defined by the fact that a full circle is 360∘360^\circ360∘ or 2π2\pi2π radians. Therefore, the conversion factor is π180\frac{\pi}{180}180π, meaning for every degree, you multiply by π180\frac{\pi}{180}180π to get the equivalent radians.
- Simplification: When converting, it’s often necessary to simplify the fraction to its lowest terms. In this case, we divided both 110 and 180 by their GCD, which was 10, to make the expression simpler.
Thus, the radian measure of 110 degrees is 11π18\frac{11\pi}{18}1811π radians
