1. 6.2 PROPERTIES of sinusoidal functions

2. HOMEFUN 
pg # 1,2, 3, 4, 9bde, 10, 12

3. 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

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

5. Investigation – IMAGINE THIS …

6. INVESTIGATION

7. INVESTIGATION

8. INVESTIGATION

9. INVESTIGATION

10. UNIT CIRCLE (DESMOS ANIMATION)
Unit Circle, Sine Function and Cosine Function
Sine Function & Unit Circle
Cosine Function & Unit Circle

11. 3D COSINE AND SINE FUNCTION
ch?v=WCxXPTtQFm4

12. MORE ANIMATIONS https://www.youtube.com/watch?v=Q55T6LeTvsA
unit-circle.html

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

14. 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 )

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

16. 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°

17. y = sinx
domain
range
coordinates of five key points are

18. 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 )

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

20. 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°

21. y = cosx
domain
range
coordinates of five key points are

22. 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 )

23. 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 )

24. EXAMPLE 1

25. 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°).

26. 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°).

27. Example 3

28. HOMEFUN 
pg # 1, 2, 3, 4, 9bde, 10, 12