To convert an angle from degrees to radians, we use the conversion formula:
[tex]\[ \text{radians} = \text{degrees} \times \left( \frac{\pi}{180} \right) \][/tex]
Given the angle is 74 degrees, we can substitute this value into the formula:
[tex]\[ \text{radians} = 74 \times \left( \frac{\pi}{180} \right) \][/tex]
First, let's break this down:
1. Calculate the fraction [tex]\(\frac{\pi}{180}\)[/tex]:
- [tex]\(\pi\)[/tex] is approximately 3.14159, so [tex]\(\frac{\pi}{180} \approx \frac{3.14159}{180} \approx 0.0174533\)[/tex].
2. Multiply 74 by 0.0174533:
- [tex]\(74 \times 0.0174533 \approx 1.29154\)[/tex].
Now we have the angle in radians as approximately 1.29154. To complete the conversion, we round this to the nearest hundredth:
[tex]\[ 1.29154 \approx 1.29 \][/tex]
Therefore, 74 degrees is approximately 1.29 radians when rounded to the nearest hundredth.
