Convert 5pi/3 radians to degrees.
Understand the Problem
The question is asking how to convert an angle measured in radians (specifically 5π/3 radians) into degrees. To solve this, we can use the conversion factor where 1 radian equals 180/π degrees.
Answer
$300$ degrees
Answer for screen readers
The angle $5\pi/3$ radians is equal to $300$ degrees.
Steps to Solve
- Identify the conversion factor
We know that 1 radian is equal to $\frac{180}{\pi}$ degrees. This conversion factor will help us change radians into degrees.
- Multiply the angle in radians by the conversion factor
To convert $5\pi/3$ radians to degrees, we multiply by the conversion factor:
$$ \text{Degrees} = \left( \frac{5\pi}{3} \right) \times \left( \frac{180}{\pi} \right) $$
- Simplify the equation
Cancel the $\pi$ in the numerator and denominator:
$$ \text{Degrees} = \frac{5 \times 180}{3} $$
- Perform the arithmetic
Now we calculate:
$$ \text{Degrees} = \frac{900}{3} = 300 $$
The angle $5\pi/3$ radians is equal to $300$ degrees.
More Information
In a circular measure, angles can be expressed in both radians and degrees. It's useful to know these conversions, especially in trigonometry and geometry, where radian measures are often used in formulas.
Tips
One common mistake is forgetting to cancel out $\pi$ when multiplying by the conversion factor. Always remember to simplify the fractions to avoid miscues in arithmetic.
