University:
High School
Course:
High School Mathematics
Academic year:

2022
Views:

363

Pages:

6
Author:

Jace Leach

9.4 Graphing Sine and Cosine Functions A. VOCABULARY & CONCEPTS y = asinb(x - h) + k a: Amplitude (height of the wave) b: Changes the period of the function h: Horizontal shift (left/right) k: Vertical shift (up/down) Periodic: The graph has a repeating pattern. Period: 2π/|b| = how often the graph repeats Amplitude = |a| = height of the wave Phase Shift = horizontal shift y = Sin X A table of values for x and y is provided: x: -2π, -3π/2, -π, -π/2, 0, π/2, π, 3π/2, 2π y: 0, -1, 0, 1, 0, -1, 0, 1, 0 A graph of the sine function is plotted based on the table of values. 7. y = cos x Table of Values: x: -2π, -3π/2, -π, -π/2, 0, π/2, π, 3π/2, 2π y: 1, 0, -1, 0, 1, 0, -1, 0, 1 Graph: A cosine wave is plotted based on the table of values. B. EXAMPLES g(x) = 4sin x a) Identify the amplitude: Amplitude = |a| = 4 b) Identify the period: Period = 2π/|b| = 2π/1 = 2π c) Graph: A sine wave with an amplitude of 4 is plotted. d) Describe the transformation of f(x) = sin x: Vertical stretch by a factor of 4 (away from the x-axis) 2. g(x) = 1/2 sin x a) Amplitude |a| = |1/2| = 1/2 b) Period 2π/|b| = 2π/1 = 2π c) Graph: A sine wave with an amplitude of 1/2 is plotted. d) Describe the transformation of f(x) = sin x Vertical shrink by a factor of 1/2 (toward the x-axis) 3. g(x) = 5 cos x Amplitude: |a| = |5| = 5 Period: 2π/|b| = 2π/1 = 2π Graph: A cosine wave with an amplitude of 5 is plotted. Description: Vertical stretch by a factor of 5.