convert 50 degrees to radians (exact answers only)
The correct answer and explanation is:
To convert degrees to radians, the formula is: radians=degrees×π180\text{radians} = \text{degrees} \times \frac{\pi}{180}
Given 50 degrees, substitute it into the formula: 50∘×π180=50π18050^\circ \times \frac{\pi}{180} = \frac{50\pi}{180}
Simplify the fraction by dividing numerator and denominator by 10: 50π180=5π18\frac{50\pi}{180} = \frac{5\pi}{18}
Therefore, 50 degrees in radians is: 5π18\boxed{\frac{5\pi}{18}}
Explanation
Radians and degrees are two units used to measure angles. Degrees divide one full rotation into 360 equal parts, while radians divide the same rotation based on the radius of a circle. One full circle is 360∘360^\circ or 2π2\pi radians.
Since 360∘=2π360^\circ = 2\pi radians, it follows that: 1∘=2π360=π180 radians1^\circ = \frac{2\pi}{360} = \frac{\pi}{180} \text{ radians}
This relationship allows converting any angle from degrees to radians by multiplying the degree value by π180\frac{\pi}{180}.
The answer remains in terms of π\pi for an exact representation, since π\pi is an irrational number. Decimal approximations lose precision and are not exact.
Simplifying the fraction reduces the result to its simplest form, making it easier to understand or use in further calculations.
In summary, converting degrees to radians involves multiplying by π180\frac{\pi}{180}, and simplifying fractions leads to exact and neat answers such as 5π18\frac{5\pi}{18} for 50 degrees.