1. Sinusoidal Functions of Sine and Cosine
On the interval from 0 to 2, the graphs of the basic sine and cosine functions have five key points: the x-intercepts, the maximum and the minimum.

4. Transformations of Sinusoidal Functions
Amplitude |A|: A controls vertical stretching/shrinking
Period p can be in radians or degrees: p is the horizontal length to complete one cycle
Horizontal shift B can be in radians or degrees: B controls horizontal stretching/shrinking
Vertical shift k:
+k , shift k units up
–k , shift k units down
Horizontal phase shift h (proportionally scaled to 2 radians or 360):
–h, shift h units right
+h, shift h units left
where, xstart corresponds with the first point of the sine or cosine cycle

5. Vertical Stretching/Shrinking of Sine and Cosine Functions
KEY TAKE-AWAY: x-intercepts are unchanged; multiply y-value of max/min by A.

8. Vertical Shifting of Sine and Cosine Functions
KEY TAKE-AWAY: If A and B remain unchanged, shift entire curve up or down.

11. Reflections of Sine and Cosine Functions
KEY TAKE-AWAY: x-intercepts are unchanged; multiply y-value of max/min by –1.

14. Horizontal Stretching/Shrinking of Sine and Cosine Functions
What if B is not 1?

15. y = sin(x)
y = sin(2x)

16. y = sin(x)
y = sin(x/2)

17. y = sin(x)
y = sin(x/3)

20. y = sin(x) y = sin(x-(/3))
Horizontal Shifting of Sine and Cosine Functions
y = sin(x)
y = sin(x-(/3))

21. y = sin(x) y = sin(x-(/2))
Horizontal Shifting of Sine and Cosine Functions
y = sin(x)
y = sin(x-(/2))

22. y = sin(x)
y = sin(x-(3/4))