DEdwards Square on Hypotenuse Square on Leg 1 Square on Leg 2 = +

 Sine  Cosine  Tangent

Prove: . .

Special Angles θ 0°0° 30 ° 45 ° 60 ° 90 ° Sin θ Cos θ Tan θ ?? ? ? ? ? ? ? ? ? ? ? ? ? ? DEdwards proof

 Sin 30 ° =  Cos 30 ° =  Tan 30 ° =  Sin 60 ° =  Cos 60 ° =  Tan 60 ° = ° 1 30 ° table

 Sin 45 ° =  Cos 45 ° =  Tan 45 ° = ° table

Trigonometric Graphs are PERIODIC i.e. they repeat themselves after a “cycle” is complete

y-intercept = 0 x-intercepts = 0 °, ±180 °, ±360 °

y-intercept = 1 x-intercepts = ±90 °, ±270 °

 Complementary Relationships  Sin x = Cos ( 90 - x)  Cos x = Sin ( 90 - x)  Tan x =

 Supplementary Relationships  Sin x = Sin ( x)  Cos x = - Cos ( x)  Tan x = - Tan ( x)

The function has ASYMPTOTES at these points

(0,1) THE UNIT CIRCLE Circle on the Cartesian plane with radius of 1 unit

(0,1) THE UNIT CIRCLE

(0,1) THE UNIT CIRCLE: 1 st Quadrant Theta θ : Angle between Terminal side & Initial side Reference Angle α : Acute Angle between Terminal Side & x-axis

(0,1) THE UNIT CIRCLE: 2 nd Quadrant Theta, θ Reference Angle α

(0,1) THE UNIT CIRCLE: 3 rd Quadrant Theta, θ Reference Angle α

(0,1) THE UNIT CIRCLE: 4 th Quadrant Theta, θ Reference Angle α

(0,1) THE UNIT CIRCLE Coordinates of points on the unit circle show (cos θ, sin θ) When the terminal side is drawn through that point

(0,1) THE UNIT CIRCLE (cos θ, sin θ) x P(a, b) θ ° O X

(0,1) THE UNIT CIRCLE Coordinates of points on the unit circle show (cos θ, sin θ) When the terminal side is drawn through that point x θ=90 ° cos90 °=0 sin90 ° =1 Hence point on circle is (0,1)

(0,1) THE UNIT CIRCLE Coordinates of points on the unit circle show (cos θ, sin θ) When the terminal side is drawn through that point x θ=180 ° Cos180° = -1 Sin 180° = 0 Hence point on circle is (-1,0)

(0,1) THE UNIT CIRCLE Coordinates of points on the unit circle show (cos θ, sin θ) When the terminal side is drawn through that point x θ=270 ° Cos 270° = 0 Sin 270° = -1 Hence point on circle is (0, -1) DEdwards

(0,1) THE UNIT CIRCLE (cos θ, sin θ) x θ=30 ° Cos 30 °= 0.866=0.9 (1dp) sin30 ° = 0.5 Hence point on circle is (0.9, 0.5) (0.9, 0.5) θ=30 °

(0,1) THE 1 st QUADRANT 0 <θ ≤ 90 For all points (x,y) x is positive & y is positive So, all points (cos θ,sin θ ) Cos θ :positive Sin θ : positive Tan θ = sin θ /cos θ=positive ll are Positive

(0,1) THE 2 nd QUADRANT 90 ° <θ ≤ 180° For all points (x,y) x is negative & y is positive So, all points (cos θ,sin θ ) Cos θ :negative Sin θ : positive Tan θ = sin θ /cos θ=negative ll are Positive INE (only) is Positive

(0,1) THE 3 rd QUADRANT 180 ° <θ ≤ 270° For all points (x,y) x is negative & y is negative So, all points (cos θ,sin θ ) Cos θ :negative Sin θ : negative Tan θ = sin θ /cos θ=positive ll are Positive INE (only) is Positive AN (only) is Positive

(0,1) THE 4 th QUADRANT 270 ° <θ ≤ 360° For all points (x,y) x is positive & y is negative So, all points (cos θ,sin θ ) Cos θ :positive Sin θ : negative Tan θ = sin θ /cos θ=negative ll are Positive INE (only) is Positive AN (only) is Positive OS (only) is Positive

(0,1) ll are Positive INE (only) is Positive AN (only) is Positive OS (only) is Positive

 “CAST” Relationships  Sin x = Sin (180 - x) = -Sin (180 + x) = Sin ( x)  Cos x = -Cos (180 - x) = -Cos (180+ x) = Cos (360 - x)  Tan x = -Tan (180 - x) = Tan (180+ x) = -Tan(360 - x)