PreCalculus: Lesson Plan * 9/05/2006

• Quickstart Green WB p.146 #66 - 82
  
• Lesson
  (4.5) Graphing Sine and Cosine Functions
  
  1. General Equation
     y = d + asin(bx - c) and y = d + acos(bx - c)
     Chart of the characteristics of a, b, c, d
  2. Examples
     p.331 #54
     y = -3cos(6x + π)
     a = -3, b = 6, c = -π, d = 0
     amplitude = |-3| = 3
     period = 2π/6 = π/3
     period - interval = [-π/6, -π/6 + π/3] = [-π/6, π/6]
     Five key points
     (-π/6, -3) Function is cosine and a < 1, so start at min = d - amplitude = 0 - 3 = -3
     (-π/12, 0) add period/4 = (π/3) /4 = π/12 to get x-coordinate
     (0, 3)
     (π/12, 0)
     (π/6, -3)
     Plot key points and connect with a smooth curve. Continue the pattern of one period-interval to get multiple periods.
     
     p.331 #50
     y = -4 + 5 cos πt/12
     a=5, b=π/12, c=0, d=-4
     amplitude = 5
     period = 2π/(π/12) = 24
     period - interval = [0/(π/12), 0/(π/12) + 24] = [0, 24]
     add 24/4 = 6 to x-coordinates
     (0, 1) cosine, a > 1, start at max = d + amp = -4 + 5 = 1
     (6, -4) add 6 to x-coordinate; y-coordinate goes to "intercept" at d=-4
     (12, -9) y-coordinate goes to min = d - amp = -4 - 5 = -9
     (18, -4) y-coordinate back to "intercept"
     (24, 1) y-coordinate back to max
     Plot five key points and connect with a smooth curve. Continue in either direction to plot more than one period.
  3. Practice p. 331 #39 - 53 Every Other Odd
     
• Homework p.331 #41 - 53 Every Other Odd