Graph y = sin (x) + 2. How does this graph compare to the graph of y = sin (x)? What is the equation of the midline of y = sin (x) + 2? Graph y = sin (x) - 3. How does this graph compare to the graph of y = sin (x)? What is the equation of the midline of y = sin (x) 3? – Explain what happens to the graph of y = sin (x) when a constant is added to sin(x). What do you notice about the midline? The standard form of the sine function is Which value (a, or is y = a sin[b(x - c)] + d. b, c, d) related to the equation of the midline? What is the equation of the midline? Graph y = sin (x) over the interval [-2π, 2π]. Graph and and compare their graphs to that of y = sin (x). What do you observe? Explain what happens when a constant is subtracted from the variable x in y = sin (x). In trigonometry, this kind of transformation is called a phase shift. A phase shift is comparable to which of the transformations you studied earlier? Which value (a, or in the equation creates a phase shift? b, c, d) y = a sin[b(x - c)] + d Based on your observations so far, sketch the graph of and then check with your calculator. Based on what you know about transformations of graphs, predict how you think the graph of y = - sin (x) will compare to the graph of y = sin (x). Check your prediction by graphing both functions on the calculator. Were you correct? Explain what happens to the graph of y = sin (x) when sin (x) is multiplied by -1. From your earlier work on transformations, what do we call this kind of transformation? Graph the parent function y = sin (x) over the interval [-2π, and compare the graphs of the 2π] following functions to its graph. y = 2 sin (x)
Graph y = sin (x) + 2. How does this graph compare to the graph of y = sin (x)? What is the equation of the midline of y = sin (x) + 2? Graph y = sin (x) - 3. How does this graph compare to the graph of y = sin (x)? What is the equation of the midline of y = sin (x) – 3? Explain what happens to the graph of y = sin (x) when a constant is added to sin(x). What do you notice about the midline? The standard form of the sine function is y = a sin[b(x - c)] + d. Which value (a, b, c, or d) is related to the equation of the midline? What is the equation of the midline? Graph y = sin (x) over the interval [-2π, 2π]. Graph and and compare their graphs to that of y = sin (x). What do you observe? Explain what happens when a constant is subtracted from the variable x in y = sin (x). In trigonometry, this kind of transformation is called a phase shift. A phase shift is comparable to which of the transformations you studied earlier? Which value (a, b, c, or d) in the equation y = a sin[b(x - c)] + d creates a phase shift? Based on your observations so far, sketch the graph of and then check with your calculator. Based on what you know about transformations of graphs, predict how you think the graph of y = - sin (x) will compare to the graph of y = sin (x). Check your prediction by graphing both functions on the calculator. Were you correct? Explain what happens to the graph of y = sin (x) when sin (x) is multiplied by -1. From your earlier work on transformations, what do we call this kind of transformation? Graph the parent function y = sin (x) over the interval [-2π, 2π] and compare the graphs of the following functions to its graph. y = 2 sin (x)
Pre-Calculus-Unit-1.docx