University:
College Entrance Preparation
Course:
ACT Preparation (Mathematics)
Academic year:

2024
Views:

116

Pages:

6
Author:

Tyshawn Shaffer

H. Algebra 2 Module 18 Review Date: ___________ Hour: ___________ 18.1 Sine and Cosine Graphs For each trigonometric function, identify the vertical stretch or compression and the horizontal stretch or compression. Then, graph the function and identify its period and amplitude. 21. y = (3/2)sin 4x Period = 2π/b = π/2 Amplitude = |a| = 3/2 [Image of the graph of y = (3/2)sin 4x] 22. y = 4sin(x/2) Period = 4π/b = 4π Amplitude = |a| = 4 [Image of the graph of y = 4sin(x/2)] 23. y = 4cos 2x Period = 2π/b = π Amplitude = |a| = 4 [Image of the graph of y = 4cos 2x] H. Algebra 2 Module 18 Review For 24-26, write an equation for the graph. 24. a = 3 b = 3 y = 3 sin(3x) [Image of a sine wave graph] 25. a = 2 b = π y = 2 cos(πx) Period = 2 [Image of a cosine wave graph] 26. a = -1/4 b = π/5 y = -(1/4) cos(πx/5) [Image of a cosine wave graph] H. Algebra 2 Module 18 Review 18.3 Translating Trigonometric Graphs For each rule given, identify the indicated points for one cycle. Then graph the function. 31. f(x) = 2sin(3x) Period = 2π/3 Starting point: (0,0) Ending point: (2π/3, 0) Middle point: (π/3, 0) Local Minimum: (π/6, -2) Local Maximum: (5π/6, 2) [Image of the graph of f(x) = 2sin(3x)] 32. f(x) = ½cos(x-π) + 1 a = ½, h = π Period = 2π Starting point: (π, 1.5) Ending point: (3π, 1.5) Middle point: (2π, 0.5) Local Minimum: (π/2, 0.5) Local Maximum: (3π/2, 1.5) [Image of the graph of f(x) = ½cos(x-π) + 1] 33. f(x) = -2cos(x-π/3) - 3 Period = 2π Starting point: (π/3, -1) Ending point: (7π/3, -1) Middle point: (4π/3, -5) Local Minimum: (π/3, -5) Local Maximum: (4π/3, -1) [Image of the graph of f(x) = -2cos(x-π/3) - 3] 34. f(x) = 3sin(2(x-π/3)) + 4 Period = π Starting point: (π/3, 4) Ending point: (4π/3, 4) Middle point: (5π/6, 7) Local Minimum: (4π/3, 1) Local Maximum: (2π/3, 7) [Image of the graph of f(x) = 3sin(2(x-π/3)) + 4] H. Algebra 2 Module 18 Review For 35-36, write a cosine or tangent function for the graph. (Hint: Use the key points and asymptotes shown on the graph.) 35. k = 5 + 1 / 2 = 3 a = 3 b = 1 y = 3 cos(x) + 2 [Image of a cosine graph] 36. b = 2 a = 3 y = 3 tan(x/2) [Image of a tangent graph]