뒤로Analyzing the Properties of a Sine Function
스터디 가이드 - 스마트 노트
자료에 맞춘 맞춤형 노트, 핵심 정의, 예시, 맥락을 확장해 제공합니다.
Q2. Given the function :
What is the amplitude?
What is the period? (Type pi for , if needed.)
What is the phase shift? (Type pi for , if needed.)
What is the mid-line? Enter your answer as an equation.
Background
Topic: Trigonometric Functions (Sine Function Transformations)
This question tests your understanding of how to analyze and interpret the parameters of a transformed sine function, including amplitude, period, phase shift, and mid-line.
Key Terms and Formulas
Amplitude: The distance from the mid-line to the maximum (or minimum) value of the function. For , amplitude is .
Period: The length of one complete cycle. For , period is .
Phase Shift: The horizontal shift of the graph. For , phase shift is (to the right if positive, to the left if negative).
Mid-line: The horizontal line that runs through the center of the graph, given by .
Step-by-Step Guidance
Identify the values of , , , and in the function .
Find the amplitude using .
Amplitude =
Calculate the period using .
Period =
Determine the phase shift using .
Phase shift =
State the mid-line using .
Mid-line:
Try solving on your own before revealing the answer!
Final Answers:
Amplitude: 3
Period: $4$
Phase shift: $3$
Mid-line:
Each value is found by applying the standard formulas for sine function transformations. The period simplifies to 4, and the phase shift simplifies to 3 units to the right.
