trig – section 4 graphing sine and cosine objectives: to graph sine and cosine curves to find...
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Trig – Section 4Graphing Sine and Cosine
Objectives: •To graph sine and cosine curves•To find amplitude, period and phase shifts.
Sine Curve:
(1,0)
(0,1)
(-1, 0)
(0,-1)
02
2
3
2
1
-1
2
3
2
2
Ex 1. Graph the following functions.
a) y = -sin x
b) y = ½ sin x 1
-12
3
2
2
1
-12
3
2
2
c) y = 1 + sin x
d) y = 2sin x1
-12
3
2
2
1
-12
3
2
2
Cosine Curve:
(1,0)
(0,1)
(-1, 0)
(0,-1)
02
2
3
2
1
-1
2
3
2
2
Ex 2. Graph the following functions.
a) y = cos x
b) y = 2 + cos x
1
-12
3
2
2
1
-12
3
2
2
c) y = -3cos x
1
-1
2
3
2
2
Class Work1. Graph y = 1 – sin x
2. Graph y = -1 + cos x
3. Graph 1sin2
y x
Amplitude and Period of Sine and Cosine Curves:
Ex 3. Find the amplitude and period of each function.
a)
b)
c)
4cos3y x
12sin
2y x
5cos3
y x
Shifted Sine and Cosine Curves:
The sine and cosine curves
have amplitude of , period , and
phase shift b.
sin ( ) cos ( )y a k x b and y a k x b
a2
k
Find the amplitude, period, and phase shift of the following.
a)
b)
c)
3sin 24
y x
2cos 43
y x
1 5sin8 1.3y x
Class WorkFind the amplitude period and phase shift of the following.
4.
5.
2 34sin
3 4y x
1 114cos
6 6y x
HW #6Graphing Worksheet
HW #7 Amplitude, Period, and Phase Shift
Worksheet All