Convert 120 degrees to radians.
Understand the Problem
The question is asking for the conversion of an angle measured in degrees (120 degrees) into radians. To convert degrees to radians, we use the formula: radians = degrees × (π/180). Applying this formula will yield the answer.
Answer
The angle of 120 degrees is equivalent to $\frac{2\pi}{3}$ radians.
Answer for screen readers
The angle of 120 degrees is equivalent to $\frac{2\pi}{3}$ radians.
Steps to Solve
- Identify the given angle in degrees
We know that the angle we want to convert is 120 degrees.
- Write down the conversion formula
To convert degrees to radians, we use the formula: $$ \text{radians} = \text{degrees} \times \frac{\pi}{180} $$
- Substitute the value of degrees into the formula
Now we substitute 120 degrees into the formula: $$ \text{radians} = 120 \times \frac{\pi}{180} $$
- Simplify the expression
Next, we simplify the expression: $$ \text{radians} = \frac{120\pi}{180} $$
- Reduce the fraction
We can reduce the fraction: $$ \frac{120}{180} = \frac{2}{3} $$
Thus, we have: $$ \text{radians} = \frac{2\pi}{3} $$
The angle of 120 degrees is equivalent to $\frac{2\pi}{3}$ radians.
More Information
When converting angles, understanding the relationship between degrees and radians is useful in many fields, including trigonometry and physics. Remember that $180$ degrees is equal to $\pi$ radians, which is key to these conversions.
Tips
- Not simplifying the fraction: After substituting, some may overlook reducing the fraction to its simplest form, which can lead to an incorrect final answer.
- Incorrect multiplication: Mistakes in multiplication when using the conversion formula can alter the outcome, so ensure to carefully calculate.
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