What is 270 degrees in radians?
Understand the Problem
The question is asking for the conversion of an angle measured in degrees (270 degrees) to its equivalent in radians. The high-level approach is to use the conversion factor that 1 degree = π/180 radians to perform the conversion.
Answer
The equivalent of 270 degrees in radians is $\frac{3\pi}{2}$.
Answer for screen readers
The angle of 270 degrees is equivalent to $\frac{3\pi}{2}$ radians.
Steps to Solve
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Identify the conversion factor
We know that $1$ degree is equivalent to $\frac{\pi}{180}$ radians. Thus, to convert degrees to radians, we will multiply the degree measurement by the conversion factor. -
Set up the conversion equation
Using the given angle of $270$ degrees, we can express the conversion to radians as follows: $$ \text{Radians} = 270 \times \frac{\pi}{180} $$ -
Simplify the expression
Now we simplify the right-hand side of the equation: $$ \text{Radians} = 270 \times \frac{\pi}{180} = \frac{270\pi}{180} $$
We can reduce this fraction by finding the greatest common divisor of $270$ and $180$, which is $90$: $$ = \frac{270 \div 90 \pi}{180 \div 90} = \frac{3\pi}{2} $$
The angle of 270 degrees is equivalent to $\frac{3\pi}{2}$ radians.
More Information
The conversion from degrees to radians is essential in mathematics and physics, particularly in fields involving trigonometric functions, which often operate in radians. Knowing that a full circle is $360$ degrees or $2\pi$ radians helps visualize these conversions.
Tips
- Not Simplifying Fractions: A common mistake is to leave the fraction unsimplified. Always look for common factors.
- Using the Wrong Conversion Factor: Ensure you use the correct relationship between degrees and radians, which is $1 \text{ degree} = \frac{\pi}{180} \text{ radians}$.
