Find the Equation of a Sine or Cosine Graph (solutions.
We continued working on graphs and characteristics of trig functions. You should have completed all of pp. 12-16 (you can do ODDS on p.15), then from pp. 17-20 choose 4 more functions to graph and complete the characteristics. Also, review pages 9-11 about characteristics of sine and cosine graphs.
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Trigonometric graphs The sine and cosine graphs. The sine and cosine graphs are very similar as they both: have the same curve only shifted along the x-axis.
To write the cosine function that fits the graph, we must find the values of A, B, C and D for the standard cosine function f x A Bx C D ( ) cos. The value of D comes from the vertical shift or midline of the graph. The midline is a horizontal line that runs through the graph having the maximum and minimum.
Lesson 6-4 Amplitude and Period of Sine and Cosine Functions 371 Example 4 y O A A If A is positive, the graph passes through the origin and heads up. If A is negative, the graph passes through the origin and heads down. y A sin 2 y O A A If A is positive, the graph crosses the y-axis at its maximum. If A is negative, the graph crosses the y.
Identify the graphs and periods of the trigonometric functions. Describe the shift of a sine or cosine graph from the equation of the function. Trigonometric functions are used to model many phenomena, including sound waves, vibrations of strings, alternating electrical current, and the motion of pendulums.
The trigonometric functions cosine, sine, and tangent satisfy several properties of symmetry that are useful for understanding and evaluating these functions. Now that we have the above identities, we can prove several other identities, as shown in the following example. Using the properties of symmetry above, we can show that sine and cosine are special types of functions.