1. Sketching y = a sin bx and y = a cos bx

2. y = sin x y = cos x x 0 30 45 60 90 120 135 150 180 210 225
240
270
300
315
330
360
sin x .5
.71
.87 1
–.5
–.71
–.87 –1 90
180
270
360 1 –1
0.5
–0.5 45
135
225
315
y = cos x x 0
30
45
60
90
120
135
150
180
210
225
240
270
300
315
330
360
cos x 1
.87
.71 .5
–.5
–.71
–.87 –1 90
180
270
360 1 –1
0.5
–0.5 45
135
225
315

3. y = sin x y = cos x x –2 –3/2 – –/2 /2  3/2 2 5/2 3 7/2 4
/2 
3/2 2
5/2 3
7/2 4
sin x
y = cos x x
–2
–3/2 –
–/2
/2 
3/2 2
5/2 3
7/2 4
cos x

4. y = sin x y = –sin x y = cos x y = –cos x x /2  3/2 2 sin x x /2
/2 
3/2 2
sin x x
/2 
3/2 2
–sin x
y = cos x
y = –cos x x
/2 
3/2 2
cos x x
/2 
3/2 2
–cos x

5. Sketching y = a sin x y = 2 sin x y = ½ sin x y = –3 sin x
/2 
3/2 2
sin x
2 sin x x
/2 
3/2 2
sin x
2 sin x x
/2 
3/2 2
sin x
2 sin x
Sketching y = a cos x
y = –2 cos x
y = ¾ cos x
y = –4 cos x x
/2 
3/2 2
cos x
–2 cos x x
/2 
3/2 2
cos x
¾ cos x x
/2 
3/2 2
cos x
–4 cos x

6. To be replaced by Ryder 1

7. Sketching y = a sin bx and y = a cos bx:
|a| = amplitude = ½(ymax – ymin) i.e., the “height” from the middle to the top
|b| = frequency = number of cycles in 2 units
P = period = the least number of positive units it takes to complete one cycle
Plot the two functions f(x) and g(x) on the same graph on 0  x  2. For each function, identify the amplitude, frequency, period and answer the number of times they intersect.
f(x) = 2 cos (3x) Amplitude: ____ Frequency: ____ Period: ____
g(x) = –2 sin (¾x) Amplitude: ____ Frequency: ____ Period: ____ 2 1 2 3 –1 –2 –3
How many times do they intersect on the interval [0, 2]? ___