Answer:
Here's what I get.
Step-by-step explanation:
Question 10
The general equation for a sine function is
y = a sin[b(x - h)] + k
Here's what the parameters control:
a = amplitude
k = vertical shift
b = the period (period = 2π/b; If period = 2π/3, b = 3)
h = horizontal shift
Reflect across y-axis (x ⟶ -x)
Your sine function will be:
[tex]\begin{array}{rllll}y = & a \text{ sin}[ & b(x- & h)] + & k)\\& \downarrow & \downarrow & \downarrow & \downarrow\\& 4 & 3 & \frac{\pi}{4} & 3\\\end{array}[/tex]
Here are the effects of each parameter.
(a) Amp = 4
Increases the amplitude by a factor of 4 (Fig. 1)
(b) Up 3
k = 3. The graph shifts up three units (Fig. 2).
(c) Period = 2π/3
Set k = 3. The period changes from 2π to 2π/3 (Fig. 3).
Notice that you now hav3 three waves between 0 and 2π, where originally you had one.
(d) Right π/4.
Set h = 4. The graph shifts right by π/4.
notice how the trough at ½π shifts to ¾π.
(e) Reflect about y-axis
Set x equal to -x. Notice how the trough at (¾π, -1) is transformed to the trough at (-¾π, -1) (Fig. 5).
Question 12
y = a cos[b(x - h)] + k
a = 2
Per = 10π/3 ⟶ b = 3/5
h = 0
k = 0
Reflect over x-axis: y ⟶ -y
(a) a = 2
The amplitude is doubled.
(b) Per = 10π/3 ⟶ b = 3/5
The period (peak-to-peak distance) lengthens to 10π/3.
(c) Reflect about x-axis (y ⟶ -y)
All peaks are transformed into troughs and vice-versa.
