To convert an angle from degrees to radians, we can use the relationship that 180 degrees is equivalent to π radians. Therefore, to convert degrees to radians, we multiply by π and then divide by 180 degrees. Using this conversion factor, we can convert 50 degrees to radians as follows:
[tex]\[ \text{Radians} = \text{Degrees} \times \frac{\pi}{180^\circ} \][/tex]
Plugging in the 50 degrees we're converting:
[tex]\[ \text{Radians} = 50^\circ \times \frac{\pi}{180^\circ} = \frac{50}{180} \pi \][/tex]
Further simplifying the fraction [tex]\( \frac{50}{180} \)[/tex], we can divide both numerator and denominator by 10 to get:
[tex]\[ \frac{50}{180} = \frac{5}{18} \][/tex]
Therefore, we have:
[tex]\[ \text{Radians} = \frac{5}{18} \pi \][/tex]
When we evaluate this expression, we find that [tex]\( \frac{5}{18} \)[/tex] is approximately 0.277777... and so, when we want to express 50 degrees in terms of π radians, we can say:
[tex]\[ 50^\circ \approx \frac{5}{18} \pi \][/tex]
And in decimal form, this is numerically equal to approximately 0.8726646259971648 radians.
So, 50 degrees is approximately 0.8726646259971648 radians, or expressed as a fraction of π, [tex]\( \frac{5}{18} \pi \)[/tex] or approximately 0.2777777777777778 π.
