Unit 8 Day 11 - Graphing Sine
and Cosine Functions
We will graph sine and cosine
using information from the
general formula
and
I will practice these graphs.
February 9, 2017
General Formula for sin functions:
y = asinb(x – c) + d
Each letter influences what the graph will look
like when you graph it.
a - vertical stretch.
|a| is called the amplitude.
gives you where the max. and the min. are
going to be.
Some books use A instead, so amplitude would
be |A|.
y = asinb(x – c) + d
A period is the horizontal distance required for
one cycle.
b - stretches or shrinks the curve in the x direction.
b > 1, the period shrinks. b < 1, the period
stretches.
also gives the number of cycles in the interval
from [0, 2π].
The period (T) of a sinusoidal curve can be found by
T = 2π/|b|.
Some books use  instead of b.
Example: Use transformations to graph each function.
y = 3sin(2x)
|a| = 3
T
2π
b
2π
T
2
Tπ
Example: Use transformations to graph each function.
 
y  cos x 
2 
2
2
T
T

b
2
|a| = 1
-4
-3
-2
-1
2
T  2 
 
T4
1
4
2
3
y = asinb(x – c) + d
c - phase shift.
Shift is to the left if c < 0
Shift is to the right if c > 0
Some books use  instead of c
d - vertical shift.
Shift is up if d > 0
Shift is down if d < 0
Example: Use transformations to graph each function.
y = -2sin(x) + 2
|a| = 2
T  2