Convert 165 degrees to radians.
Understand the Problem
The question is asking how to convert an angle measured in degrees (165 degrees) to its equivalent in radians. The conversion from degrees to radians involves using the formula: radians = degrees × (π / 180).
Answer
The equivalent of 165 degrees in radians is \( \frac{11\pi}{12} \).
Answer for screen readers
The equivalent of 165 degrees in radians is ( \frac{11\pi}{12} ).
Steps to Solve
-
Identify the degrees to convert
We start with the angle given in degrees, which is 165 degrees. -
Use the conversion formula
To convert degrees to radians, use the formula:
$$ \text{radians} = \text{degrees} \times \frac{\pi}{180} $$ -
Substitute the degree value into the formula
Substituting 165 degrees into the formula gives:
$$ \text{radians} = 165 \times \frac{\pi}{180} $$ -
Simplify the fraction
To simplify, calculate ( \frac{165}{180} ):
$$ \frac{165}{180} = \frac{11}{12} $$
So, we have:
$$ \text{radians} = \frac{11\pi}{12} $$ -
Write the final answer
The final answer is ( \frac{11\pi}{12} ) radians.
The equivalent of 165 degrees in radians is ( \frac{11\pi}{12} ).
More Information
When converting degrees to radians, it's important to remember that there are ( 2\pi ) radians in a full circle of ( 360 ) degrees. Thus, each degree is equivalent to ( \frac{\pi}{180} ) radians.
Tips
- A common mistake is forgetting to use the conversion factor ( \frac{\pi}{180} ) and just using ( \pi ).
- Another mistake is not simplifying the fraction ( \frac{165}{180} ) fully, which leads to incorrect values in the final answer.
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