chapter 5: trigonometric functions and graphs section 5.1: … · 2018. 9. 9. · section...
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Chapter 5: Trigonometric Functions and GraphsSection 5.1: Graphing Sine and Cosine Functions
Periodic Function: a function for which the dependent variable takes on the same set of values over and over again as the independent variable changes
Sinusoidal Function: a periodic function that looks like waves
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Important Terms for Sinusoidal Functions
period: the change in the xcorresponding to the cycle of the function. A cycle is a portion of the graph from one point to the point at which the graph starts to repeat
amplitude, sinusoidal axis, local max/local min
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Graph of y = sin xThere's 5 key points we associate with the graph, since these points will help us determine the characteristics of the graph (amplitude, domain, range, period, range and zeros, sinusoidal axis). However we are not limited to these points.
x 0
y 0 1 0 1 0
Amplitude
period
Domain
range
max value:
min value:
yintercept:
xintercepts:
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y = sin x
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Determining the Amplitude of a Sine Function
y = 2sinx y= 0.5sinx
• Any function of the form y = af(x) is related to y = f(x) by a vertical stretchfactor of
• for the function y = asinx, the amplitude is
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Determining the Period of a Transformed Sine Function
y= sin 2x y=sin 0.5x
A function of the form y = f(bx) is related to y = f(x) by a horizontal stretch by a factor of about the yaxis.
Changing the value of b affects the period of a sinusoidal function.
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Reflections
y = sin2x
y = ‐sin2x y = sin (‐2x)
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Example 1: Sketch the graph of y = ‐3sin2x for at least one cycle. Determine the amplitude, period, max and min values, x‐intercepts, y‐ intercepts, domain and range and equation of sinusoidal axis.
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Pg 233 #4ac, #5 a,c, #7, 9a,c, #11b,c,d,
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Graph of y = cos x
x 0
y 1 0 1 0 1
#4b,d,5b,d,8,9bd,11a
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Section 5.2: Transformations
Example 1: Sketch the graph of the function
State the period, amplitude, sinusoidal axis, domain and range.
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Example 2: Sketch the graph of the function
State the period, amplitude, sinusoidal axis, domain and range.
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Example 3: Given
State the amplitude, sinusoidal axis (horizontal central axis), vertical displacement, local max/min, period, phase shift, domain and range
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Pg 250 #1a,c,e,f, #2(don't graph)a,c,f #3a, #4 #5
#14
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Determining the Equation from a Graph
y = (sin (x ) +
y = (cos (x ) +
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Example 1: The graphs below shows the function y = f(x).A) Write the equation in the form y = a sin b(xc) + d, a > 0
B) Write the equation in the form y = a cos b(xc) + d, a > 0
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Pg 250 #5, 6ac, 7, 14, 15, 16
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Contextual Problems
Example 1:
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pg 248 your turn, 10a, 23,24
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