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6.2 PROPERTIES of sinusoidal functions
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HOMEFUN pg # 1,2, 3, 4, 9bde, 10, 12
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Sinusoidal function a periodic function whose graph looks like smooth symmetrical waves where any portion of the wave can be horizontally translated onto another portion of the curve; graphs of sinusoidal functions can be created by transforming the graph of the function y = sinx or y = cosx
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Investigation the unit circle & the PRIMARY trigonometric functions
x2 + y2 = 1
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Investigation – IMAGINE THIS …
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INVESTIGATION
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INVESTIGATION
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INVESTIGATION
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INVESTIGATION
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UNIT CIRCLE (DESMOS ANIMATION)
Unit Circle, Sine Function and Cosine Function Sine Function & Unit Circle Cosine Function & Unit Circle
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3D COSINE AND SINE FUNCTION
ch?v=WCxXPTtQFm4
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MORE ANIMATIONS https://www.youtube.com/watch?v=Q55T6LeTvsA
unit-circle.html
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y = sinx (y=sin) y = cosx (y=cos) graph maximum minimum equation of axis amplitude period domain range key coordinates
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y = sinx (y=sin) y = cosx (y=cos) graph maximum (90°, 1) (0°, 1) minimum (270°, -1) (180°, -1 ) equation of axis y= 0 amplitude A = 1 period P = 360° domain { x | x R } range { y | -1 y 1, y R } key coordinates (0°,0) (90°, 1) (180°, 0 ) (270°, -1) (360°, 0 ) (0°,1) (90°, 0) (180°, -1 ) (270°, 0) (360°, 1 )
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y = sinx (y=sin) maximum value is maximum occurs at x =
minimum value is minimum occurs at x= equation of the axis amplitude period
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y = sinx (y=sin) maximum value is 1 maximum occurs at x = 90°
minimum value is -1 minimum occurs at x= 270° equation of the axis is y= 0 amplitude A = 1 period P = 360°
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y = sinx domain range coordinates of five key points are
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y = sinx domain { x | x R } range { y | -1 y 1, y R }
the coordinates of five key points are (0°,0) (90°, 1) (180°, 0 ) (270°, -1) (360°, 0 )
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y = cosx (y=cos) maximum value is maximum occurs at x =
minimum value is minimum occurs at x= equation of the axis amplitude period
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y = cosx (y=cos) maximum value is 1 maximum occurs at x = 0° & 360°
minimum value is -1 minimum occurs at x= 180° equation of the axis y =0 amplitude A = 1 period P = 360°
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y = cosx domain range coordinates of five key points are
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y = cosx domain { x | x R } range { y | -1 y 1, y R }
the coordinates of five key points are (0°,1) (90°, 0) (180°, -1 ) (270°, 0) (360°, 1 )
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y = sinx (y=sin) y = cosx (y=cos) graph maximum (90°, 1) (0°, 1) minimum (270°, -1) (180°, -1 ) equation of axis y= 0 amplitude A = 1 period P = 360° domain { x | x R } range { y | -1 y 1, y R } key coordinates (0°,0) (90°, 1) (180°, 0 ) (270°, -1) (360°, 0 ) (0°,1) (90°, 0) (180°, -1 ) (270°, 0) (360°, 1 )
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EXAMPLE 1
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EXAMPLE 2 f(x) = 4sin(3x) +2 Graph the function on a graphing calculator or Desmos. Is the function periodic? If it is, is it sinusoidal? From the graph, determine the period, theequation of the axis, the amplitude, and the range. Calculate f (20°).
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EXAMPLE 2 f(x) = 4sin(3x) +2 Graph the function .
Is the function periodic? If it is, is it sinusoidal? From the graph, determine the period, theequation of the axis, the amplitude, and the range. Calculate f (20°).
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Example 3
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HOMEFUN pg # 1, 2, 3, 4, 9bde, 10, 12
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