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TRIG FUNCTIONS
TRIG FUNCTIONS
Most text books will tech trig functions using only local angles and thus only operating in Quadrant 1. Using the global angle allows the trig functions to operate across the entire global 360 turn.
TRADITIONAL
TRIG
TRADITIONAL
TRIG
1st Quadrant local definitions.
SOH * CAH * TOA
Everything is based on local angles and their respective projections of adjacent side, opposite side, and hypotenuse.
This is the version most of us were probably taught.
FULL 360 TRIG DEFINITIONS
360 TRIG
360 TRIG
UNIT CIRCLE: Using a 1 unit length for the radius of a circle
Radius is therefore the hypotenuse
Cosine is the projection of the 1 unit length onto the X-Axis for a given angle.
Sine is projection of the 1 unit length onto the Y Axis for a given angle.
Tangent is the slope of the 1 unit length for a given angle.
Direction: 0 Degrees
Unit Length = 1
Projection on X Axis = 1
(Going to the right is positive)
Cos (0) = 1
Projection on Y Axis = 0
Sin (0) = 0
Slope = 0 (its Flat)
Direction: 90 Degrees
Unit Length = 1
Projection on X Axis = 0
Cos (90) = 0
Projection on Y Axis = 1
(Going up is positive)
Sin (90) = 1
Slope = Infinity (its a vertical wall)
Direction: 180 Degrees
Unit Length = 1
Projection on X Axis = -1
(Going to the left is negative)
Cos (180) = -1
Projection on Y Axis = 0
Sin (180) = 0
Slope = 0 (its Flat)
Direction: 270 Degrees
Unit Length = 1
Projection on X Axis = 0
Cos (270) = 0
Projection on Y Axis = -1
(Going down is negative)
Sin (270) = -1
Slope = Infinity (its a vertical wall)
Direction: 30 Degrees
Unit Length = 1
Projection on X Axis = +0.866
Cos (30) = +0.866
Projection on Y Axis = +0.5
Sin (0) = +0.5
Slope = rise/run = +0.5/+0.866
Slope =+0.577
Tan (30) = +0.577
Direction: 130 Degrees
Unit Length = 1
Projection on X Axis = -0.643
Cos (130) = -0.643
Projection on Y Axis = +0.766
Sin (130) = +0.766
Slope = rise/run = =+0.766/-0.643
Slope =-1.192
Tan (130) = -1.192
Direction: 230 Degrees
Unit Length = 1
Projection on X Axis = -0.643
Cos (230) = -0.643
Projection on Y Axis = -0.766
Sin (230) = -0.766
Slope = rise/run = =-0.766/-0.643
Slope =+1.192
Tan (130) = +1.192
Direction: 300 Degrees
Unit Length = 1
Projection on X Axis = +0.5
Cos (300) = +0.5
Projection on Y Axis = -0.866
Sin (300) = -0.866
Slope = rise/run = =-0.866/+0.5
Slope =-1.732
Tan (130) = -1.732
Angles in Quad 1
X-Projections (+)
Y-Projections (+)
Slope (+/+ = +)
Angles in Quad 2
X-Projections (-)
Y-Projections (+)
Slope (+/- = -)
Angles in Quad 3
X-Projections (-)
Y-Projections (-)
Slope (-/- = +)
Angles in Quad 4
X-Projections (+)
Y-Projections (-)
Slope (-/+ = -)
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