find an angle between 0 and & 2 pi that is coterminal with - 11 over 24 pi
coterminal angles are obtained by adding or subtracting multiples of 2π.
(2π is one rotation)
did you mean -11/(24π) or (-11/24)π
I will guess you meant the last.
-11/24 π is appr. -1.4
so let's add 2π
-11/24 π + 2π = (37/24)π
To find an angle that is coterminal with -11/24π within the range of 0 and 2π, you can use the concept of coterminal angles.
First, let's understand what coterminal angles are. Coterminal angles are two angles that have the same initial and terminal sides when drawn in standard position, but differ by a multiple of 2π (or 360 degrees). In other words, they end up at the same position after completing a full revolution around the origin.
To find a coterminal angle, you can add or subtract any multiple of 2π from the given angle. In this case, the given angle is -11/24π.
To make our calculations easier, let's convert the fraction to a decimal value:
-11/24π ≈ -1.4488π
Now, we can add or subtract any multiple of 2π from -1.4488π.
Adding 2π:
-1.4488π + 2π ≈ 0.5512π
Subtracting 2π:
-1.4488π - 2π ≈ -3.4488π
Both 0.5512π and -3.4488π are coterminal angles with -11/24π.
However, the angles were specified to be within the range of 0 and 2π. To convert the negative angle to a positive angle within this range, we can add 2π to it.
-3.4488π + 2π ≈ -1.4488π
Therefore, the angle between 0 and 2π that is coterminal with -11/24π is approximately -1.4488π or roughly 3.456 radians.