- Quickstart: Algebra I Workbook p.145 #26 - 50 Simplifying Radicals
- Lesson
(4.5) Graphing Sine and Cosine Functions- 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.
- Example: Sketch the graph of the following
- Practice p. 330 #20, 22, 26, 34
- Translations of Sine and Cosine Curves (p.327 - 328)
- Homework
p.330 - 331 #15 - 33 x 3's, #39 - 54 x 3's
16 years ago
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