1. pencil, red pen, highlighter, packet, notebook, calculator
U8P2D2
Have out:
Bellwork:
Sketch one positive period of each sine function (on the worksheet).
(Scale your x–axis with radians)
a) y = sin x
b) y = –sin x
c) y = 3 sin x
total:

2. y 1 x a) y = sin x -1 y 1 x b) y = –sin x -1 y 3 x c) y = 3 sin x
+2 graph
a) y = sin x
+1 label y–axis -1
+2 label x–axis y x 1
+2 graph
b) y = –sin x -1
+1 label y–axis
+2 label x–axis y x 3
+2 graph
c) y = 3 sin x
+1 label y–axis
total:
+2 label x–axis -3

3. unit circle
Practice # 2: Fill in the coordinates of the _________ for every multiple of x
( , ) y

4. The Cosine Function: Fill in the table with the decimal equivalent for cosθ. 1
0.71
–0.71 –1
–0.71
0.71 1
Plot the points (θ, cosθ) on the graph below to make the cosine function. 1 –1 

5. 1 –1  QI
QII
QIII
QIV
positive
In QI, cos θ is _______. cos θ = 0 at θ = _____.
negative
In QII, cos θ is _______. cos θ reaches a minimum at θ = ____.
negative
In Q III, cos θ is _______. cos θ = 0 at θ = ____.
In Q IV, cos θ is _______. cos θ reaches a maximum at θ = ___.
positive

6. 2
Practice # 3: Sketch ____ periods of y = cos x. y x 1 -1
1 period
1 period

7. Practice # 4: Sketch y = sin x and y = cos x on the same axes
Practice # 4: Sketch y = sin x and y = cos x on the same axes. (Use different colors for each graph!) Label all intercepts. Draw vertical, dashed lines to indicate the quadrantal angles (quadrant divisions). y x 1 -1

8. > < < > > > < < y x 1 -1 QI: QII: QIII: QIV:
cos x  0
sin x  0
cos x  0
sin x  0
cos x  0
sin x  0
<
cos x  0
sin x  0
>
>
>
<
<

9.  If 0 ≤ x < 2π , then for what values of x is:
( , ) y
sin x = cos x
x = ,

10. y x 1 -1
 If 0 ≤ x < 2π , then for what values of x is:
sin x = cos x
cos x > sin x
sin x > cos x
x = , ,

11. For both y = sin x and y = cos x, the period length is ___ or ___.2π
360˚
Frequency
________ is We say the ________ is __.
frequency 1
frequency 2
y = sin 2x would have a _________ of __, so y = sin 2x would do its cycle _____ as fast. y = sin 2x would do ____ cycles in 2π .
twice 2 y 1 x -1

12. Practice # 5: Sketch one period of y = sin 2x.π
The period of y = sin 2x is ___. y x 1 1 2 3 4 -1
Half the period
Half again
Then count up

13.  would have a frequency of ___,
so would do ______ a cycle in 2π. y 1 x -1

14. Practice # 6: Sketch one period of .
The period of is ____. 4π y x 1 1 2 3 4 -1
Half the period
Half again
Then count up

15.  For y = a sin bx,
b = ____________ (# of cycles per 2π)
frequency
a = ____________
amplitude
The ______ of y = a sin x is __________ or __________.
period
There is an ________ relationship between b and p:
inverse
big
small
_______ b, _________ p
_______ p, _________ b
big
small
 The same is also true for y = a cos x.

16. Practice # 7: Sketch one period of each function. Use radian measure.y x 2 2
b = ____
p = ____ 4 -2 1 2 3 4
Half the period
Half again
Then count up

17. Practice # 7: Sketch one period of each function. Use radian measure.b) y x 1 1
b = ____
p = ____ -1 1 2 3 4
Half the period
Half again
Then count up

18. Practice # 7: Sketch one period of each function. Use radian measure.y x
b = ____
p = ____ 3 1 2 3 4
Half the period
Half again
Then count up

19. Practice # 7: Sketch one period of each function. Use radian measure.y x 4 4
b = ____
p = ____ -4 1 2 3 4
Half the period
Half again
Then count up

20. Work on the rest of the packet, but let’s do some of the exercises in Problem #2.

21. 2. Determine a y = a sin bx or y = a cos bx for each function.1
____, b = ____, p = ____, y = ________ 2π 2
sin
(1x)

22. 2. Determine a y = a sin bx or y = a cos bx for each function.–6
cos 6
____, b = ____, p = ____, y = ___________ 6π

23. 2. Determine a y = a sin bx or y = a cos bx for each function.
1 period
1 period x
sin
(16x) 16
____, b = ____, p = ____, y = __________

24. y x