Convert 300 degrees to radians.
Understand the Problem
The question is asking to convert an angle measured in degrees (300 degrees) into radians. To do this, we will use the conversion factor that π radians is equal to 180 degrees.
Answer
The angle of $300$ degrees is equal to $\frac{5\pi}{3}$ radians.
Answer for screen readers
The angle of $300$ degrees is equal to $\frac{5\pi}{3}$ radians.
Steps to Solve
- Identify the conversion factor
We know that $180$ degrees is equivalent to $\pi$ radians. This fact will help us convert degrees to radians.
- Set up the conversion equation
To convert degrees to radians, we use the following formula: $$ \text{radians} = \text{degrees} \times \frac{\pi}{180} $$
- Substitute the given value
Now, we will substitute $300$ degrees into the equation: $$ \text{radians} = 300 \times \frac{\pi}{180} $$
- Simplify the expression
We can simplify the expression: $$ \text{radians} = \frac{300\pi}{180} $$
- Reduce the fraction
Now, simplify the fraction: $$ \frac{300\pi}{180} = \frac{5\pi}{3} $$
The angle of $300$ degrees is equal to $\frac{5\pi}{3}$ radians.
More Information
Converting between degrees and radians is essential in trigonometry and calculus. Knowing how to perform these conversions allows for easier manipulation of angles in various mathematical contexts.
Tips
- Forgetting to multiply by $\frac{\pi}{180}$ instead of dividing.
- Not simplifying the final fraction, which can lead to a less straightforward answer.
