1. Aim: How do we sketch y = A(sin Bx) and
y = A(cos Bx)?
Do Now: If y = 2sin 2x, fill in the table below
HW: Handout

2. y = 2sin2x

3. In the form of
When we multiply x, the measure of the angle, by some value, B, we change the frequency of the curve.
Frequency: The number of complete curves in every 2π radians.
This means we have more “complete” curves in the interval
So the frequency of y = sin 2x is 2

4. or In
A implies the amplitude
To find the amplitude of sine or cosine function, we simply take absolute value of A ( )
We only use positive number for amplitude. For example: the amplitude of y = 2 sin x and y = –2 sin x are both 2
the amplitude of y = ½ sin x and y = -1/2 sin x are both ½
The rule to find the period is

5. For y = sin x, the frequency is 1 since the value of B is 1, and the period is 2. That means there is only one complete curve within 2 radians also means to have a complete curve, the angle measure is 2 radians.
The amplitude is 1 and the period is
The amplitude is 2 and the period is

6. Determining the Period and Amplitude of y = a sin bx
Given the function y = 3sin 4x, determine the period
and the amplitude.
The period of the function is
Therefore, the period is
The amplitude of the function is | a |.
Therefore, the amplitude is 3.
y = 3sin 4x

7. Writing the Equation of the Periodic Function
Amplitude p
b = 2
= 2
Therefore, the equation as a function of sine is
y = 2sin 2x.

8. Writing the Equation of the Periodic Function
Amplitude
Period
4 p
= 3
b = 0.5
Therefore, the equation as a function of cosine is
y = 3cos 0.5x.

9. a) Sketch the graph of , over
b) Find the value(s) of x in the interval so that the
value of
(1) a maximum (2) a minimum (3) 0

10. Find the amplitude and period for the following functions:b) c)