30 degrees to radians in terms of pi.
Understand the Problem
The question is asking to convert an angle measurement from degrees to radians, specifically expressing the result in terms of pi. To do this, we use the conversion factor that π radians is equivalent to 180 degrees.
Answer
$$ \text{Radians} = \frac{x\pi}{180} $$
Answer for screen readers
To convert an angle $x$ degrees to radians, the answer is: $$ \text{Radians} = \frac{x\pi}{180} $$
Steps to Solve
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Identify the angle in degrees Start with the angle you need to convert. For example, let's say the angle is $x$ degrees.
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Use the conversion factor Use the conversion factor that states $\pi$ radians is equivalent to 180 degrees. This means we can set up a ratio to convert degrees to radians: $$ \text{Radians} = x \times \frac{\pi}{180} $$
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Simplify the expression Now, multiply the angle in degrees by the fraction. This gives you: $$ \text{Radians} = \frac{x\pi}{180} $$
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Express the result in terms of $\pi$ The final result will be expressed as a fraction of $\pi$. For example, if $x$ was 90 degrees: $$ \text{Radians} = \frac{90\pi}{180} = \frac{\pi}{2} $$
To convert an angle $x$ degrees to radians, the answer is: $$ \text{Radians} = \frac{x\pi}{180} $$
More Information
This formula allows you to convert any degree measurement into radians easily. Knowing the relationship between degrees and radians is essential in trigonometry and various applications of physics and engineering.
Tips
- Confusing the conversion factor: Sometimes people forget that $180$ degrees corresponds to $\pi$ radians.
- Failing to simplify the fraction: It's important to simplify the final result, such as reducing $\frac{90\pi}{180}$ to $\frac{\pi}{2}$.
