DETERMINE DIRECTION

Determine the Global Angle from a Local

Reference Axis = 90 degrees
Local Angle = 35 degrees Counterclockwise
Direction = Outward

Global Angle = 90 + 35 + 0 = 125 degrees

NOTES:
Rotation: If the local angle is going clockwise from the referenced axis, this would be a negative angle.

Direction: If the arrow is pointing towards the origin instead of away from the origin, add/subtract 180.

CHECK:
The arrow is pointing into Quadrant 2, so the angle should be between 90-180. We have 125 degrees.
We do not know if we are right, but we know we are not wrong yet.

Determine the Global Angle from a ratio

Reference Axis = 0 Degrees
(The ratio triangle is shown between the vector and the reference axis)

Opposite value: 5
Adjacent value: 12
Local Angle = tan-1(5/12) = 22.620
Direction = Inward

Global Angle = 0 + 22.62 + 180
Global Angle = 202.62 degrees

CHECK:
The arrow is pointing into Quadrant 3, so the angle should be between 180-270. We have 202.62 degrees.
We do not know if we are right, but we know we are not wrong yet.

Determine the Global Angle from cogo

Point A (-3,7)
Point B (10,-8)

Direction A>B ... therefore change = B-A

Change X = 10 - (-3) = 13
Change Y = -8 - (7) = -15

Step 1: Calc = Tan-1(Change Y / Change X)
Step 1: Calc = Tan-1 (-15/13) = -49.0856

Step 2: If Change X is negative, add 180.
Step 2: Change X is (+), therefore add 0.
Step 2: -49.0856

Step 3: If Step 2 is negative, add 360
Step 3: -49.0856 + 360 = 310.9144

Global Angle = 310.9144 degrees

CHECK:
The arrow is pointing into Quadrant 4, so the angle should be between 270-360. We have 310.9144 degrees.
We do not know if we are right, but we know we are not wrong yet.