Convert 22.5 degrees to radians.
Understand the Problem
The question is asking to convert 22.5 degrees into radians. This involves using the conversion factor that π radians is equal to 180 degrees.
Answer
The conversion of 22.5 degrees to radians is \(\frac{1}{8}\pi\) or approximately 0.3927 radians.
Answer for screen readers
The conversion of 22.5 degrees to radians is (\frac{1}{8}\pi) or approximately 0.3927 radians.
Steps to Solve
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Identify the conversion factor To convert degrees to radians, we use the conversion factor: $$ \text{radians} = \frac{\pi}{180} \times \text{degrees} $$
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Substitute the value Now, we substitute 22.5 degrees into the equation: $$ \text{radians} = \frac{\pi}{180} \times 22.5 $$
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Calculate the multiplication Perform the multiplication in the equation: $$ \text{radians} = \frac{22.5\pi}{180} $$
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Simplify the fraction Now, simplify the fraction: $$ \text{radians} = \frac{22.5}{180}\pi = \frac{1}{8}\pi $$
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Final result in decimal or fractional form You can leave the answer in terms of $\pi$ or convert it to a decimal (optional). In decimal form: $$ \frac{1}{8}\pi \approx 0.3927 $$
The conversion of 22.5 degrees to radians is (\frac{1}{8}\pi) or approximately 0.3927 radians.
More Information
Converting between degrees and radians is a common task in trigonometry and calculus. Radians are often preferred in calculus because they provide a natural measure of angles for cyclic functions.
Tips
- A common mistake is forgetting to multiply by the conversion factor. Always remember to include both parts of the conversion formula.
- Another mistake could be not simplifying the fraction, resulting in a less readable answer.
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