Convert 510 degrees to radians.
Understand the Problem
The question is asking to convert 510 degrees into radians. To do this, we will use the conversion factor that π radians is equal to 180 degrees.
Answer
The conversion of $510$ degrees to radians is $\frac{51\pi}{18}$.
Answer for screen readers
The conversion of $510$ degrees to radians is $\frac{51\pi}{18}$.
Steps to Solve
- Identify the conversion factor
We need to use the conversion factor that states $180$ degrees is equal to $\pi$ radians.
- Set up the conversion equation
To convert degrees to radians, we use the formula: $$ \text{radians} = \text{degrees} \times \frac{\pi \text{ radians}}{180 \text{ degrees}} $$
- Insert the values into the equation
Now, substitute $510$ degrees into the equation: $$ \text{radians} = 510 \times \frac{\pi}{180} $$
- Simplify the fraction
Next, simplify the fraction: $$ \frac{510}{180} = \frac{51}{18} $$
- Multiply by π
Finally, multiply the simplified fraction by $\pi$ to find the result in radians: $$ \text{radians} = \frac{51\pi}{18} $$
The conversion of $510$ degrees to radians is $\frac{51\pi}{18}$.
More Information
The radian is a standard unit of angular measure used in many areas of mathematics. The result $\frac{51\pi}{18}$ can also be approximated as about $8.90$ radians for practical uses.
Tips
- A common mistake is to forget the conversion factor or to mix up the numerator and denominator. Always remember to use the ratio $\frac{\pi}{180}$ when converting degrees to radians.
