Convert 2.5 radians to degrees.
Understand the Problem
The question is asking to convert an angle measurement from radians to degrees. To do this, we can use the conversion factor where 1 radian is approximately 57.2958 degrees.
Answer
$114.59$ degrees
Answer for screen readers
The angle conversion gives approximately $114.59$ degrees from $2$ radians.
Steps to Solve
- Identify the angle in radians
Start with the angle that you want to convert. For example, let's say the angle is $x$ radians.
- Use the conversion factor
To convert from radians to degrees, multiply the radian measure by the conversion factor ( \frac{180}{\pi} ).
This means you will use the formula:
$$ \text{Degrees} = x \cdot \frac{180}{\pi} $$
- Plug in the value and calculate
If the angle was, for example, 2 radians, substitute ( x ) with 2:
$$ \text{Degrees} = 2 \cdot \frac{180}{\pi} $$
- Calculate the numerical value
Now, perform the multiplication to find the numerical value for degrees.
Using ( \pi \approx 3.14159 ):
$$ \text{Degrees} \approx 2 \cdot \frac{180}{3.14159} $$
Now calculate:
$$ \text{Degrees} \approx 2 \cdot 57.2958 \approx 114.5916 $$
- Round if necessary
Depending on the context, you may want to round your answer. For example, rounding ( 114.5916 ) to two decimal places gives you ( 114.59 ) degrees.
The angle conversion gives approximately $114.59$ degrees from $2$ radians.
More Information
To convert radians to degrees, always remember the factor ( \frac{180}{\pi} ). This is crucial as it helps you transition between these two measurement systems easily. Also, knowing that ( \pi ) is about ( 3.14159 ) will aid in making the conversion more straightforward.
Tips
- Forgetting to multiply by the conversion factor ( \frac{180}{\pi} ) when converting.
- Using an incorrect approximation for ( \pi ) which can lead to slightly inaccurate results.
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