4.5 graphs of sine and cosine functions
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
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
The Sine Curve
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
The Cosine Curve
Section 4.5, Figure 4.44, Key Points in the Sine and Cosine
Curves, pg. 288
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
Find the period and amplitude
p. 294 #1 y x3 2sin
Find the period and amplitude
p. 294 #11 yx
1
4
2
3cos
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
Reference Graphs y = sin x y = cos x
