Definition of an angle Terminal Ray Counter clockwise

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Definition of an angle Terminal Ray + Counter clockwise - clockwise Terminal Ray Initial

Definition of an angle Terminal Ray + Counter clockwise - clockwise Terminal Ray Initial Ray

Coterminal angles – angles with a common terminal ray Terminal Ray Initial Ray

Coterminal angles – angles with a common terminal ray Terminal Ray Initial Ray

Coterminal angles – angles with a common terminal ray Terminal Ray Initial Ray

Coterminal angles – angles with a common terminal ray Terminal Ray Initial Ray

Radian Measure

Radian Measure

Definition of Radians C= 2πr C= 2π radii C= 2π radians 360 o =

Definition of Radians C= 2πr C= 2π radii C= 2π radians 360 o = 2π radians 180 o = π radians r 1 Radian 57. 3 o r

Unit Circle – Radian Measure

Unit Circle – Radian Measure

Unit Circle – Radian Measure

Unit Circle – Radian Measure

Unit Circle – Radian Measure Degrees

Unit Circle – Radian Measure Degrees

Converting Degrees ↔ Radians Converts degrees to Radians Recall Converts Radians to degrees more

Converting Degrees ↔ Radians Converts degrees to Radians Recall Converts Radians to degrees more examples

Trigonometric Ratios

Trigonometric Ratios

Basic ratio definitions Hypotenuse Opposite Leg Reference Angle θ Adjacent Leg

Basic ratio definitions Hypotenuse Opposite Leg Reference Angle θ Adjacent Leg

Circle Trigonometry Definitions = s u i r d Ra Adjacent Leg = x

Circle Trigonometry Definitions = s u i r d Ra Adjacent Leg = x reciprocal functions (x, y) Opposite Leg = y

Unit - Circle Trigonometry Definitions s iu ad =1 R Adjacent Leg = x

Unit - Circle Trigonometry Definitions s iu ad =1 R Adjacent Leg = x 1 (x, y) Opposite Leg = y

Unit Circle – Trig Ratios (-, +) (-, -) Skip π/4’s sin (+, +)

Unit Circle – Trig Ratios (-, +) (-, -) Skip π/4’s sin (+, +) (+, -) Reference Angles cos tan

Unit Circle – Trig Ratios sin (-, +) (+, +) (-, -) (+, -)

Unit Circle – Trig Ratios sin (-, +) (+, +) (-, -) (+, -) cos tan

Unit Circle – Trig Ratios (-, +) sin cos tan (+, +) (0 ,

Unit Circle – Trig Ratios (-, +) sin cos tan (+, +) (0 , 1) Quadrant Angles (-1, 0) (1, 0) 0 /2π (0, -1) (-, -) View π/4’s (+, -) sin cos tan 0 1 0 Ø 0 -1 0 Ø

Unit Circle – Radian Measure (-, +) sin cos tan (+, +) Quadrant Angles

Unit Circle – Radian Measure (-, +) sin cos tan (+, +) Quadrant Angles 1 (-, -) (+, -) Degrees 0 /2π sin cos tan 0 1 0 Ø 0 -1 0 Ø

A unit circle is a circle with a radius of 1 unit. For every

A unit circle is a circle with a radius of 1 unit. For every point P(x, y) on the unit circle, the value of r is 1. Therefore, for an angle θ in the standard position:

Graphing Trig Functions f ( x ) = A sin bx

Graphing Trig Functions f ( x ) = A sin bx

Amplitude is the height of graph measured from middle of the wave. Amplitude Center

Amplitude is the height of graph measured from middle of the wave. Amplitude Center of wave f ( x ) = A sin bx

f ( x ) = cos x A = ½ , half as tall

f ( x ) = cos x A = ½ , half as tall

f ( x ) = sin x A = 2, twice as tall

f ( x ) = sin x A = 2, twice as tall

Period of graph is distance along horizontal axis for graph to repeat (length of

Period of graph is distance along horizontal axis for graph to repeat (length of one cycle) f ( x ) = A sin bx

f ( x ) = sin x B = ½ , period is 4π

f ( x ) = sin x B = ½ , period is 4π

f ( x ) = cos x B = 2, period is π

f ( x ) = cos x B = 2, period is π

Trigonometry Hipparchus, Menelaus, Ptolemy Special The Pythagoreans Graphs Right Triangles Rene’ Des. Cartes

Trigonometry Hipparchus, Menelaus, Ptolemy Special The Pythagoreans Graphs Right Triangles Rene’ Des. Cartes

Reference Angle Calculation nd Quadrant rd 4 th 2 3 Quadrant Angles Return

Reference Angle Calculation nd Quadrant rd 4 th 2 3 Quadrant Angles Return

Unit Circle – Degree Measure 90 120 60 45 135 150 30 180 0/360

Unit Circle – Degree Measure 90 120 60 45 135 150 30 180 0/360 330 210 225 315 300 240 270 Return

Unit Circle – Degree Measure (-, +) 90 120 sin (+, +) tan 30

Unit Circle – Degree Measure (-, +) 90 120 sin (+, +) tan 30 45 60 45 135 cos 60 150 30 Quadrant Angles 180 0/360 1 210 225 330 sin cos tan 0/360 0 1 0 315 240 300 90 1 0 Ø (-, -) (+, -) 180 0 -1 0 270 -1 0 Ø 270 Return

Ex. # 3 Ex. # 4 Ex. # 5 Ex. # 6 return

Ex. # 3 Ex. # 4 Ex. # 5 Ex. # 6 return

Circle Trigonometry Definitions – Reciprocal Functions = s u i r d Ra Adjacent

Circle Trigonometry Definitions – Reciprocal Functions = s u i r d Ra Adjacent Leg = x return (x, y) Opposite Leg = y

Unit Circle – Radian Measure 1

Unit Circle – Radian Measure 1