How many radians is 300 degrees?
Understand the Problem
The question is asking how many radians correspond to 300 degrees. To solve this, we need to use the conversion factor between degrees and radians, which is π radians = 180 degrees.
Answer
$\frac{5\pi}{3}$
Answer for screen readers
The final answer is $\frac{5\pi}{3}$ radians.
Steps to Solve
- Identify the conversion factor
The relationship between degrees and radians is given by the conversion factor:
$$ \pi \text{ radians} = 180 \text{ degrees} $$
- Set up the equation for conversion
To convert degrees to radians, we use the formula:
$$ \text{radians} = \text{degrees} \times \frac{\pi \text{ radians}}{180 \text{ degrees}} $$
In this case, we will substitute 300 degrees into the formula.
- Perform the calculation
Substituting 300 degrees into the equation gives us:
$$ \text{radians} = 300 \times \frac{\pi}{180} $$
Now we simplify:
$$ \text{radians} = \frac{300\pi}{180} $$
- Simplify the fraction
Next, we simplify $\frac{300}{180}$:
$$ \frac{300}{180} = \frac{5}{3} $$
So the equation becomes:
$$ \text{radians} = \frac{5\pi}{3} $$
The final answer is $\frac{5\pi}{3}$ radians.
More Information
Converting between degrees and radians is a common task in trigonometry and calculus. Knowing how to easily convert will help in understanding angles in different contexts, such as in circular motion or wave functions.
Tips
- A common mistake is forgetting to use the correct conversion factor, leading to incorrect results. Always remember that $180$ degrees is equivalent to $\pi$ radians.
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