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4.5 Graphs of Sine and Cosine Functions AmplitudePeriodTranslations
The graph of f(x)=sin x Domain all Real numbers Range -1 to 1
The graph of f(x)=sin x Sin x is an odd function
Graph of f(x) = -sin x
Graph of the f(x) = Cos x Domain: All real numbers Range: -1 to 1
Graph of the f(x) = Cos x Cos x is an even function
The red graph is Sin and the blue is Cos
Amplitude changes the Range
Since Amplitude is a distance, it is always positive. To find it: the absolute value of the Maximum minus the Minimum divide by two. Amp is written before the function y = a*sin x
Amplitude changes the Range Max 7; Min - 1 Amp.
Period (wave length) The distance before the function repeats its value. y = sin bx; here b is 1.
Period (wave length) y = sin 2x b = 2
Translation to move the graph of the functiony = sin (x + c): moves Right or Left Here is
Translation to move the graph of the functiony = sin x + d moves up or down Here is
With all the translations The sine function is f(x) = d + a sin b(x +c) The cosine function is f(x) = d + a cos b(x +c)
Applet for the Sine function sine.htm
Homework Page 307 – 310 #3, 9, 14, 20, 26, 32, 41, 49, 71, 78
Homework Page 307 – 310 #7, 12, 17, 23, 27, 36, 45, 60, 76, 86
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1.Find the solutions. 2.Find the Vertex and Max (-1, 0) (5, 0) (2, 10)
Write equation or Describe Transformation. Write the effect on the graph of the parent function down 1 unit1 2 3 Stretch by a factor of 2 right 1 unit.
Next Back Esc Sine and Cosine Graphs Reading and Drawing Sine and Cosine Graphs Some slides in this presentation contain animation. Slides will be more.
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1 To find the x-intercepts of y = f (x), set y = 0 and solve for x. INTERCEPTS AND ZEROS To find the y-intercepts of y = f (x), set x = 0; the y-intercept.
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Next Back Tangent and Cotangent Graphs Reading and Drawing Tangent and Cotangent Graphs Some slides in this presentation contain animation. Slides will.
A Preview of Transformations Objective: Identify the transformations from one function to another.
Topic 4 Periodic Functions & Applications II 1.Definition of a radian and its relationship with degrees 2.Definition of a periodic function, the period.
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And Visa Versa. Suppose: v 1 (t) = 1V sin ( t) v 2 (t) = 1V cos ( t) The sine wave reaches its maximum when t = 90 o, but the cosine reaches its.
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Trigonometric Graphs Click to continue. You are already familiar with the basic graph of y = sin x o. There are some important points to remember. 360.
2-5 Absolute Value Functions and Graphs. Vertex Maximum or minimum of the graph For the equation, the vertex is at.
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