What are the expression describing all the angle that are coterminal with 72 degree?
(72+360k)° for any integer k
To find all the angles that are coterminal with 72 degrees, we need to add or subtract multiples of 360 degrees. This is because two angles are coterminal if they have the same initial and terminal side when drawn in standard position.
First, let's add a multiple of 360 degrees to 72 degrees:
72 + 360n, where n is an integer
By substituting different values of n, we can find the coterminal angles in one direction. For example:
n = 1: 72 + 360(1) = 432 degrees
n = 2: 72 + 360(2) = 792 degrees
n = 3: 72 + 360(3) = 1152 degrees
Now, let's subtract multiples of 360 degrees from 72 degrees:
72 - 360n, where n is an integer
By substituting different values of n, we can find the coterminal angles in the other direction. For example:
n = 1: 72 - 360(1) = -288 degrees
n = 2: 72 - 360(2) = -648 degrees
n = 3: 72 - 360(3) = -1008 degrees
Therefore, the expressions describing all the angles that are coterminal with 72 degrees are:
72 + 360n and 72 - 360n, where n is an integer.