Final answer:
To convert the angle θ = 257π/360 radians to degrees, multiply by the conversion factor 1 radian = 57.3 degrees.
Step-by-step explanation:
To convert an angle from radians to degrees, you can use the fact that π radians is equal to 180 degrees. The conversion factor from radians to degrees is thus \( \frac{180°}{π} \). Given the angle \( θ = \frac{257π}{360} \) radians, we want to convert it to degrees.
Here's the step-by-step process: 1. Multiply \( θ \) by the conversion factor \( \frac{180°}{π} \) to get the angle in degrees. \[ θ_{\text{degrees}} = θ_{\text{radians}} × \frac{180°}{π} \]
2. Substitute \( θ = \frac{257π}{360} \) into the equation: \[ θ_{\text{degrees}} = \frac{257π}{360} × \frac{180°}{π} \]
3. The π in the numerator and denominator cancel out: \[ θ_{\text{degrees}} = \frac{257}{360} × 180° \]
4. Multiply through: \[ θ_{\text{degrees}} = \frac{257 × 180°}{360} \]
5. Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 360: \[ θ_{\text{degrees}} = \frac{257 × 180°}{360} = \frac{257}{2}° \]
6. Calculate the exact value: \[ θ_{\text{degrees}} = 128.5° \] So the angle \( θ = \frac{257π}{360} \) radians is exactly 128.5 degrees.