 # Definition of an angle Terminal Ray Counter clockwise

• Slides: 36  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  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 Degrees Converting Degrees ↔ Radians Converts degrees to Radians Recall Converts Radians to degrees more examples Trigonometric Ratios Basic ratio definitions Hypotenuse Opposite Leg Reference Angle θ Adjacent Leg 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 1 (x, y) Opposite Leg = y Unit Circle – Trig Ratios (-, +) (-, -) Skip π/4’s sin (+, +) (+, -) Reference Angles cos tan Unit Circle – Trig Ratios sin (-, +) (+, +) (-, -) (+, -) cos tan 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 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 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   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 ) = sin x A = 2, twice as tall 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 ) = cos x B = 2, period is π  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 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 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 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