Final answer:
To find the angle between 0 and 2π that is coterminal with 1020°, convert degrees to radians, subtract multiples of 2π to get a value within the range, and add 2π if necessary to maintain a positive measure. The result is 5π/3 radians.
Step-by-step explanation:
To determine the angle between 0 and 2π radians that is coterminal with 1020°, we first need to convert 1020° into radians. Since 180° is equivalent to π radians, we can perform the conversion as follows:
1020° × (π rad / 180°) = 5.65π rad
Now, angles are coterminal if they differ by a multiple of 2π radians. Since 5.65π rad is greater than 2π rad, we subtract multiples of 2π rad until we get an angle within the required range:
5.65π - 2π × 2 = 1.65π rad
This angle is still greater than 2π, so we subtract another 2π:
1.65π - 2π = -0.35π rad
Finally, since angles are positive when measuring counter-clockwise, we need to add 2π to get a positive angle:
-0.35π + 2π = 1.65π rad
1.65π rad is equivalent to 5π/3 rad when expressed as a fraction, which corresponds to the answer choice (b) 5 times π over 3.