Final answer:
To find the degree measure of an object that has traveled 32pi/5 radians, we convert the radians to degrees using the formula degrees = radians × (180/pi), resulting in 1152 degrees.
Step-by-step explanation:
If an object travels in a circle 32pi/5 radians, we can convert this radian measure to degrees to find its position relative to where it started. The conversion from radians to degrees is based on the fact that a complete revolution is 2π radians (or 360 degrees).
To convert radians to degrees, we use the formula: degrees = radians × (180/π). Therefore, to convert 32pi/5 radians to degrees:
- 32pi/5 radians × (180/π) = 32 × 36 = 1152 degrees
So, the object would be at a degree measure of 1152 degrees relative to where it started. Since 1152 is more than 360, it indicates that the object has made more than 3 complete revolutions.