Convert 30 degrees to radians.
Understand the Problem
The question asks for a conversion from degrees to radians. To convert degrees to radians, you multiply the degree value by π/180.
Answer
The angle of $60^\circ$ converts to $\frac{\pi}{3}$ radians.
Answer for screen readers
The angle of $60^\circ$ converts to $\frac{\pi}{3}$ radians.
Steps to Solve
- Identify the Degree Value
First, find out the degree value you want to convert. For example, let's say we want to convert $60^\circ$ to radians.
- Set Up the Conversion Factor
Use the conversion factor from degrees to radians, which states that to convert degrees to radians, you multiply by $\frac{\pi}{180}$.
- Perform the Calculation
Multiply the degree value by the conversion factor:
$$ radians = 60^\circ \times \frac{\pi}{180} $$
- Simplify the Expression
Now simplify the equation:
$$ radians = 60 \times \frac{\pi}{180} = \frac{60\pi}{180} = \frac{\pi}{3} $$
- State the Result
The final answer in radians is $\frac{\pi}{3}$.
The angle of $60^\circ$ converts to $\frac{\pi}{3}$ radians.
More Information
When converting between degrees and radians, it's useful to remember that a full circle is $360^\circ$, which is equivalent to $2\pi$ radians. Therefore, $180^\circ$ is equivalent to $\pi$ radians, making the conversion easier.
Tips
- Forgetting to use the conversion factor $\frac{\pi}{180}$.
- Confusing radians and degrees; always double-check which unit you are working with.
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