Convert 390 degrees to radians.
Understand the Problem
The question is asking to convert an angle measurement from degrees to radians. This involves using the conversion factor where 180 degrees is equal to π radians.
Answer
For $D$ degrees, the angle in radians is given by $D \times \frac{\pi}{180}$.
Answer for screen readers
The angle in radians is given by the formula:
$$ \text{Radians} = D \times \frac{\pi}{180} $$
For example, for $D = 90$ degrees, the answer would be:
$$ \frac{\pi}{2} $$
Steps to Solve
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Identify the degree measurement Determine the angle in degrees that you want to convert. For example, let's say the angle is $D$ degrees.
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Use the conversion factor To convert degrees to radians, you use the conversion factor that states $180$ degrees is equal to $\pi$ radians. This can be set up as a fraction:
$$ \text{Radians} = D \times \frac{\pi}{180} $$
- Perform the multiplication Multiply the degree measurement by the conversion factor. For example, if $D = 90$ degrees:
$$ \text{Radians} = 90 \times \frac{\pi}{180} $$
- Simplify the result Simplify the expression to find the result in radians. Following the previous example:
$$ \text{Radians} = \frac{90\pi}{180} = \frac{\pi}{2} $$
The angle in radians is given by the formula:
$$ \text{Radians} = D \times \frac{\pi}{180} $$
For example, for $D = 90$ degrees, the answer would be:
$$ \frac{\pi}{2} $$
More Information
Converting between degrees and radians is essential in trigonometry and calculus, as many mathematical functions use radians for angle measures. It's also useful in programming and various fields of science and engineering.
Tips
- Forgetting the conversion factor: Always remember that $180$ degrees corresponds to $\pi$ radians.
- Incorrect simplification: Ensure to simplify the fraction correctly, as it's easy to make errors when handling $\pi$.
- Not using a calculator correctly: If you convert to radians using a calculator, make sure the calculator is set to the correct mode.
