What angle between 0 and 360 degrees is coterminal with 86 degrees?

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In geometry, two angles are considered coterminal if they share the same terminal side when drawn in standard position. This means they can differ by any multiple of 360 degrees.

To find an angle that is coterminal with 86 degrees, we can use the following formula:

coterminal angle = original angle + (n * 360)

Where:

  • original angle is the angle in question (in this case, 86 degrees),
  • n is any integer (positive or negative).

First, let’s find a positive coterminal angle:

  • Set n = 1:
    • coterminal angle = 86 + (1 * 360) = 86 + 360 = 446 degrees

Since 446 degrees is greater than 360 degrees, we need to find a coterminal angle that falls within the range from 0 to 360 degrees. To do this:

  • Set n = -1:
    • coterminal angle = 86 + (-1 * 360) = 86 - 360 = -274 degrees

This negative angle isn’t what we’re looking for, so let’s check its absolute value:

coterminal angle = 360 - 274 = 86 degrees

This means that the angle coterminal with 86 degrees that falls within the range of 0 to 360 is simply:

86 degrees

Conclusively, the only angles that are coterminal with 86 degrees within the desired range are 86 degrees itself and any angle addition or subtraction that results in multiples of 360 degrees away from it.

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