How do you find an angle between 0 degrees and 360 degrees that is coterminal with 600 degrees, and an angle between 0 and 2 that is coterminal with 1120 degrees?

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To find an angle that is coterminal with a given angle, you can add or subtract full rotations (360 degrees for degrees or 2π radians for radians) until you bring the angle within the desired range.

Part A: Finding a Coterminal Angle for 600 Degrees

The first step is to determine how many full circles (360 degrees) fit into 600 degrees. You can do this by subtracting 360 from 600:

600 - 360 = 240

This result tells us that 240 degrees is coterminal with 600 degrees. To ensure that the angle is within the range of 0 to 360 degrees, we can check:

  • 240 is greater than 0
  • 240 is less than 360

Thus, the coterminal angle for 600 degrees within the range of 0 to 360 degrees is 240 degrees.

Part B: Finding a Coterminal Angle for 1120 Degrees

Next, we aim to find an angle between 0 and 2 (or between 0 and 2π radians) that is coterminal with 1120 degrees. To convert degrees to radians, we can use the following conversion:

Radians = Degrees * (π / 180)

First, convert 1120 degrees to radians:

Radians = 1120 * (π / 180) ≈ 19.63

Now we need to find a coterminal angle that falls between 0 and 2π (approximately 6.28). We can do this by subtracting multiples of 2π until we are within this range:

19.63 - 6.28 ≈ 13.35

Since 13.35 is still greater than 6.28, we subtract 2π (or about 6.28) again:

13.35 - 6.28 ≈ 7.07

Finally, we subtract 2π again:

7.07 - 6.28 ≈ 0.79

Thus, the angle that is coterminal with 1120 degrees, staying within the range of 0 and 2π, is approximately 0.79 radians.

In summary:

  • Coterminal angle for 600 degrees: 240 degrees
  • Coterminal angle for 1120 degrees: 0.79 radians

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