To convert an angle from radians to degrees, multiply the radian measure by 180π\frac{180}{\pi}π180.
Formula:
Degrees=Radians×180π\text{Degrees}=\text{Radians}\times \frac{180}{\pi}Degrees=Radians×π180
Explanation:
- One full circle is 2π2\pi 2π radians, which equals 360 degrees.
- Therefore, π\pi π radians equals 180 degrees.
- Using this relationship, multiplying radians by 180π\frac{180}{\pi}π180 converts the angle into degrees.
Example:
Convert 5π3\frac{5\pi}{3}35π radians to degrees:
5π3×180π=5×1803=300∘\frac{5\pi}{3}\times \frac{180}{\pi}=\frac{5\times 180}{3}=300^\circ 35π×π180=35×180=300∘
Additional notes:
- One radian is approximately 57.296 degrees.
- This method works for any radian value, including fractions and multiples of π\pi π.
This conversion is widely used in trigonometry and geometry for switching between these two angle measurement units
