What characteristic of sinusoidal functions appears to be affected when the variable x is multiplied by a constant in y = sin (x)? In trigonometry, we say this transformation has affected the period of y = sin (x). What is the period of y = sin (x)? What is the period of y = sin (2x)? What is the period of y = sin (3x)? What is the period of y = sin (4x)? What is the period of y = sin (½ x)? The transformation that affects the period is comparable to a horizontal stretch (or shrink). Based on your observations, if y = sin (5x) is graphed over [0, how many cycles will 2π], occur. What is the period of y = sin (5x)? In the standard form of the sine function it is the value that affects y = a sin[b(x - c)] + d, b the period. If you graphed y = sin (bx) where b >0, how many cycles do you predict will occur over [0, What is the period of y = sin (bx) where b >0? 2π]? Using your conjectures from above, sketch by hand the graph of these functions. Use your calculator to check your graphs. 2 y = 2 sin(x)+2 b. y = sin (2x) The general form of the cosine function is The graph of the parent y = a cos[b(x - c)] + d. function y = cos (x) is affected in a similar way by and Make a prediction about the a, b, c, d. graphs of the following functions and then check by graphing the function on the calculator.
What characteristic of sinusoidal functions appears to be affected when the variable x is multiplied by a constant in y = sin (x)? In trigonometry, we say this transformation has affected the period of y = sin (x). What is the period of y = sin (x)? What is the period of y = sin (2x)? What is the period of y = sin (3x)? What is the period of y = sin (4x)? What is the period of y = sin (½ x)? The transformation that affects the period is comparable to a horizontal stretch (or shrink). Based on your observations, if y = sin (5x) is graphed over [0, 2π], how many cycles will occur. What is the period of y = sin (5x)? In the standard form of the sine function y = a sin[b(x - c)] + d, it is the value b that affects the period. If you graphed y = sin (bx) where b >0, how many cycles do you predict will occur over [0, 2π]? What is the period of y = sin (bx) where b >0? Using your conjectures from above, sketch by hand the graph of these functions. Use your calculator to check your graphs. y = 2 sin(x)+2 b. y = 2 sin (2x) The general form of the cosine function is y = a cos[b(x - c)] + d. The graph of the parent function y = cos (x) is affected in a similar way by a, b, c, and d. Make a prediction about the graphs of the following functions and then check by graphing the function on the calculator.
Pre-Calculus-Unit-1.docx