The answers are:
Part 1: 5π/4 radians
Part 2: 3.92 radians
Part 3: -229π/20 radians
Part 1:
Coterminal angles: Coterminal angles are angles in standard position (angles with the initial side on the positive x-axis) that share the same terminal side.
Finding a coterminal angle: To find a positive coterminal angle with (13/4)π radians, we can subtract multiples of 2π radians.
Subtracting 2π radians: (13/4)π - 2π = (13π - 8π) / 4 = 5π / 4.
The least positive angle that is coterminal with (13/4)π radians is 5π/4 radians.
Part 2:
Following the same principles as part 1: To find a positive coterminal angle with 10.2 radians, we can subtract a multiple of 2π radians.
Subtracting 2π radians: 10.2 - 2π = 10.2 - 6.28 ≈ 3.92.
The least positive angle that is coterminal with 10.2 radians is 3.92 radians.
Part 3:
Negative angles and coterminality: We can also apply the concept of coterminal angles to negative angles.
Subtracting 2π radians: -189π/20 - 2π = -189π - 40π / 20 = -229π / 20.
The least positive angle that is coterminal with -189π/20 radians is -229π/20 radians.