Question

you board a ferris wheel at ground level and travel to the very top, when it stops to allow more riders to get on. how many degrees has the ferris wheel rotated? 180° complete what is the radian equivalent for 180°? 2π radians π radians π/2 radians done

Explanation:

First Sub - Question (Ferris Wheel Rotation Degrees)

When you board a Ferris wheel at ground level and go to the very top, the Ferris wheel has rotated a semicircle. A full circle is \(360^{\circ}\), so a semicircle is \(\frac{360^{\circ}}{2}=180^{\circ}\).

Step 1: Recall the conversion formula

The formula to convert degrees to radians is \( \text{radians}=\text{degrees}\times\frac{\pi}{180^{\circ}} \).

Step 2: Substitute the value of degrees

We want to convert \(180^{\circ}\) to radians. Substitute \( \text{degrees} = 180^{\circ}\) into the formula: \( \text{radians}=180^{\circ}\times\frac{\pi}{180^{\circ}} \).

Step 3: Simplify the expression

The \(180^{\circ}\) in the numerator and denominator cancels out, leaving us with \( \pi \) radians.

Answer:

\(180^{\circ}\) (already marked as correct in the problem)

Second Sub - Question (Radian Equivalent of \(180^{\circ}\))