Aim #36: How do we graph transformations of sine and cosine?
HW Due Tuesday 12/13
Speed Quiz Thursday 12/8 AND Test Wednesday 12/14
Do Now:
Sketch the graph of y = sin x and y = cos x
y= a sin (b(x + c)) + d
y = a cos (b(x + c)) + d
a = amplitude- |a|- the distance from the midline to the highest or
lowest value of the graph. If a is negative that means it
is a reflection in the x-axis.
b = frequency- the number of whole curves in 2 π
period= 2π how long it takes to see one full curve
|b|
d = midline- your vertical shift. (your 'imaginary' x axis). the line that
is half way between the maximum (which is ML + a) and
minimum (which is ML- a) values. To find the Midline find
the average of the max and min points.
c = phase- shift- your translation in the x- axis. we will count boxes
to help us graph this.
In the interval [0, 2π], graph y = 2sin(x).
Graph y =sin(x) + 2 on the interval 0 ≤ x ≤ 2π
What is your parent function? What transformation took place?
In the interval [0, 2π], graph y = 2sin(x).
In the interval [0, 3π], graph
What is your parent function? What transformation took place?
Inthe
theinterval
interval[0,[0,2π],
2π],
graph y = 2sin(x).
In
graph
What is your parent function? What transformation took place?
Inthe
theinterval
interval[0,
[0,2π],
2π],graph
graphy y=cos(x
= 2sin(x).
In
- π).
What is your parent function? What transformation took place?
In
the interval
[0, of
2π],
Graph
one period
y =graph
cos (2yπ=x)2sin(x).
What is your parent function? What transformation took place?
Inthe
theinterval
interval[-π,
[0, π],
2π],
graph
y = 2sin(x).
In
graph
y =-cosx.
What is your parent function? What transformation took place?
In the interval [0, 2π], graph y = 2sin(x).
In the interval [0, 2π], graph
What is your parent function? What transformation took place?
theinterval
interval
[0,
2π],
graph y = 2sin(x).
InInthe
[-π
, π],
graph
What is your parent function? What transformation took place?
In the interval [0, 2π], graph y = 2sin(x).
In the interval [-π, π], graph
What is your parent function? What transformation took place?
In the interval [0, 2π], graph y = 2sin(x).
In the interval [0, 2π], graph
What is your parent function? What transformation took place?