6.2 PROPERTIES of sinusoidal functions

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Presentation transcript:

6.2 PROPERTIES of sinusoidal functions

HOMEFUN  pg 363-364 # 1,2, 3, 4, 9bde, 10, 12

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

Investigation the unit circle & the PRIMARY trigonometric functions x2 + y2 = 1

Investigation – IMAGINE THIS …

INVESTIGATION

INVESTIGATION

INVESTIGATION

INVESTIGATION

UNIT CIRCLE (DESMOS ANIMATION) Unit Circle, Sine Function and Cosine Function https://www.geogebra.org/m/Z26WBQgM Sine Function & Unit Circle https://www.desmos.com/calculator/kxfekf0kgb Cosine Function & Unit Circle https://www.desmos.com/calculator/s8jg20tfws

3D COSINE AND SINE FUNCTION https://www.youtube.com/wat ch?v=WCxXPTtQFm4

MORE ANIMATIONS https://www.youtube.com/watch?v=Q55T6LeTvsA https://www.mathsisfun.com/algebra/trig-interactive- unit-circle.html

y = sinx (y=sin) y = cosx (y=cos) graph maximum minimum equation of axis amplitude period domain range key coordinates

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 )

y = sinx (y=sin) maximum value is maximum occurs at x = minimum value is minimum occurs at x= equation of the axis amplitude period

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°

y = sinx domain range coordinates of five key points are

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 )

y = cosx (y=cos) maximum value is maximum occurs at x = minimum value is minimum occurs at x= equation of the axis amplitude period

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°

y = cosx domain range coordinates of five key points are

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 )

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 )

EXAMPLE 1

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°).

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°).

Example 3

HOMEFUN  pg 363-364 # 1, 2, 3, 4, 9bde, 10, 12