PreCalculus: Lesson Plan * 8/31/2006

• Quickstart: Algebra I Workbook p.145 #26 - 50 Simplifying Radicals
• Lesson
  (4.5) Graphing Sine and Cosine Functions
  
  1. Translations of Sine and Cosine Curves (p.327 - 328)
     The graphs of y=asin( bx - c) and y = acos( bx - c) have a horizontal shift of c/b.
     
     • Example: Sketch the graph of the following
       a) y = cos(x - π/2)
       Remember the five key points for y = cosx are
       (0, 1) [max]
       (π/2, 0) [int]
       (π, -1) [min]
       (3π/2, 0) [int]
       (2π, 1) [max]
       c/b = π/2 / 1 = π/2
       The graph shifts π/2 to the right. The key points become
       (π/2, 1) [max]
       (π, 0) [int]
       (3π/2, -1) [min]
       (2π, 0) [int]
       (5π/2, 1) [max]
       
       b) y = 2sin (2x + π/2)
       Remember the key points for y = sinx are
       (0, 0) [int]
       (π/2, 1) [max]
       (π, 0) [int]
       (3π/2, -1) [min]
       (2π, 0) [int]
       c/b = π/2 / 2 = π
       The graph shifts to the left π and the amplitude is 2 so the max has its y-coordinate at 2 and the min has its y-coordinate at -2. The five key points become
       (-π/4, 0) [int]
       (0, 2) [max]
       (π/4, 0) [int]
       (π/2, -2) [min]
       (3π/4, 0) [int]
     • Adding or subtracting onto the entire trig function results in a vertical shift.
       y = 1 - 0.5sin(0.5x - π)
       will have a vertical shift UP of 1 unit.
       
  2. Practice p. 330 #20, 22, 26, 34
     
• Homework
  p.330 - 331 #15 - 33 x 3's, #39 - 54 x 3's