4.5 Graphs of Sine and Cosine Functions
• Students will sketch the graphs of basic sine and cosine functions.
• Students will use amplitude and period to help sketch the graphs of sine and cosine functions.
• Students will sketch translations of graphs of sine and cosine functions.
• Students will use sine and cosine functions to model real-life data.
Evaluate the Sine Curve using the unit circle
Copyright © Houghton Mifflin Company. All rights reserved. Digital Figures, 4–17
Section 4.5, Figure 4.42, Graph of Sine Curve, pg. 287
x
y (0, 1)
90°2
(–1, 0)
180°
(0, –1)
270°32
(1, 0)0° 0
60° 3
31 ,2 2
45°4
2 2,2 2
30° 6
3 1,2 2
330°116
3 1,2 2
315°74
2 2,2 2
300°53
31 ,2 2
23
120°
31 ,2 2
34
135°
2 2,2 2
56
150°
3 1,2 2
210°76
3 1,2 2
225°5
4
2 2,2 2
240°43
31 ,2 2
Evaluate the Cosine Curve using the unit circle
Copyright © Houghton Mifflin Company. All rights reserved. Digital Figures, 4–18
Section 4.5, Figure 4.43, Graph of Cosine Curve, pg. 287
x
y (0, 1)
90°2
(–1, 0)
180°
(0, –1)
270°32
(1, 0)0° 0
60° 3
31 ,2 2
45°4
2 2,2 2
30° 6
3 1,2 2
330°116
3 1,2 2
315°74
2 2,2 2
300°53
31 ,2 2
23
120°
31 ,2 2
34
135°
2 2,2 2
56
150°
3 1,2 2
210°76
3 1,2 2
225°5
4
2 2,2 2
240°43
31 ,2 2
Graph y = sin x and y = 2 sin x on your graphing calculator. Notice that the height of the hump has changed. In the equation y = a sin x is known as the amplitude of the function.
a
Graph y = cos x and y = cos 2x on your graphing calculator. Notice that the length of the curve has changed. In the equation y = cos bx, b affects the period of the function. Using sin and cos P
b
2
Describe the relationship between the graphs of f and g. Consider amplitudes, periods, and shifts.
p. 294 #15f x x
g x x
( ) sin
( ) sin( )
Describe the relationship between the graphs of f and g. Consider amplitudes, periods, and shifts.
p. 294 #21f x x
g x x
( ) sin
( ) sin
2
5 2
Sketch the graphs of f and g in the same coordinate plane. (Include two full periods.)
p. 294 #27f x x
g x x
( ) sin
( ) sin
4
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