(2 ) the curve. We then extend the graph in either = cos , we multiply the y x y-coordinates direction to obtain the graph shown below. of We plot these five points and fill in the graph of the five key points for = cos by = 1 .The y x A five key points are (0,1) π , ⎛ ⎞ (π π ⎞ , ,1) , ⎛ , −1⎞ , ⎛ 3π ⎜ 4 ⎟ ⎜ 2 ⎟ ⎜ ⎟ 4 ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ We plot these five points and fill in the graph of the curve. We then extend the graph in either direction to obtain the graph shown below. 52. Comparing (ω ) = cos y A x , = ⎛ ⎞ 2 cos 1 to y x ⎜ 4 ⎟ ω = 2 and = 1 . Therefore, the A 4 we find ⎝ ⎠ = 8π . amplitude is 2 = 2 and the period is 2π 1/ 4 Because the amplitude is 2, the graph of = 2 cos ⎛ 1 ⎞ y x −2 will lie between and 2 on ⎜ 4 ⎟ ⎝ ⎠ the Because the period is 8π , one cycle y-axis.
y = cos (2 x ) , we multiply the y-coordinates of We plot these five points and fill in the graph of the curve. We then extend the graph in either direction to obtain the graph shown below. the five key points for five key points are y = cos x by A = 1 .The (0,1) , ⎛ π ⎞ , ⎛ π , −1⎞ , ⎛ 3π ⎞ , (π ,1) ⎜ 4 ⎟ ⎜ 2 ⎟ ⎜ 4 ⎟ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ We plot these five points and fill in the graph of the curve. We then extend the graph in either direction to obtain the graph shown below. 52. Comparing y = 2 cos ⎛ 1 x ⎞ to y = A cos (ω x ) , ⎜ 4 ⎟ we find ⎝ ⎠ A = 2 and ω = 1 . Therefore, the 4 amplitude is 2 = 2 and the period is 2π 1/ 4 Because the amplitude is 2, the graph of = 8π . y = 2 cos ⎛ 1 x ⎞ will lie between −2 and 2 on ⎜ 4 ⎟ ⎝ ⎠ the y-axis. Because the period is 8π , one cycle
62514-0132318806_ISM_02-1.docx