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Graphs of Cosine Section 4-5
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Objectives I can determine all key values for 6 trig functions
I can graph cosine functions I can determine amplitude, period, and phase shifts of cosine functions
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Graph of the Cosine Function
To sketch the graph of y = cos x first locate the key points. These are the maximum points, the minimum points, and the intercepts. 1 -1 cos x x Then, connect the points on the graph with a smooth curve that extends in both directions beyond the five points. A single cycle is called a period. y x y = cos x Cosine Function
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Properties of Sine and Cosine Functions
The graphs of y = sin x and y = cos x have similar properties: 1. The domain is the set of real numbers. (-∞, ∞) 2. The range is the set of y values such that 3. The maximum value is 1 and the minimum value is –1. 4. The graph is a smooth curve. 5. Each function cycles through all the values of the range over an x-interval of 6. The cycle repeats itself indefinitely in both directions of the x-axis. Properties of Sine and Cosine Functions
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Graphing Trig Functions
Find the period of the function We will use the following to graph: “x” represents radians “” represents degrees Example: sin x versus sin Determine the key points (Make data table) Intercepts Maximum points Minimum points
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y = cos x Start HIGH, middle, low, middle, high
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Example: Sketch the graph of y = 3 cos x on the interval [–, 4].
Partition the interval [0, 2] into four equal parts. Find the five key points; graph one cycle; then repeat the cycle over the interval. max x-int min 3 -3 y = 3 cos x 2 x y x (0, 3) ( , 3) ( , 0) ( , 0) ( , –3) Example: y = 3 cos x
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θ 90 180 270 360 Cos 1 -1 2 Cos 2 -2 Rx 45 degrees Left -45 45 135 225 315 90 180 270 360 -90 -180 -270 -360
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White Board
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White Board
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Homework Trig Value Table WS 9-2
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