Question

The least positive angle that is coterminal with (13/4)pi radians is ____ radians. The least positive angle that i’d coterminal with 10.2 radians is ____ radians. The least positive angle that is coterminal with (-189/20)pi radians is ____ radians.

Answer 1

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.

Answer 2

Remember that

Coterminal angles are angles in standard position (angles with the initial side on the positive x -axis) that have a common terminal side.

so

To find a positive and a negative angle coterminal with a given angle, you can add and subtract 360° if the angle is measured in degrees or 2π if the angle is measured in radians

N 1

we have

13π/4

subtract 2π

(13π/4)-2π=9π/4

The answer to Part 1 is 9π/4 radians

N 2

we have 10.2 radians

so

10.2 -2π=10.20-6.28=3.92 radians

The answer to part 2 is 3.92 radians

N 3

we have

-189π/20 radians

subtract 2π radians

-189π/20-2-189π/20-2π=-229π/20 radians

The answer to part 3 is -229π/20 radians