교과서 질문
Graph each function over a one-period interval.
y = 2 tan (¼ x)
712
views
Ch. 4 - Graphs of the Circular Functions
Lial12th EditionTrigonometryISBN: 9780136552161
Not the one you use?Change textbookSelect a different textbook
Table of contents
- Ch. R - Algebra Review381
- Ch. 1 - Trigonometric Functions188
- Ch. 2 - Acute Angles and Right Triangles168
- Ch. 3 - Radian Measure and The Unit Circle155
- Ch. 4 - Graphs of the Circular Functions100
- Ch. 5 - Trigonometric Identities238
- Ch. 6 - Inverse Circular Functions and Trigonometric Equations158
- Ch. 7 - Applications of Trigonometry and Vectors148
- Ch. 8 - Complex Numbers, Polar Equations, and Parametric Equations15
5장, 문제 19
Match each function in Column I with the appropriate description in Column II.
I
y = 3 sin(2x - 4)
II
A. amplitude = 2, period = π/2, phase shift = ¾
B. amplitude = 3, period = π, phase shift = 2
C. amplitude = 4, period = 2π/3, phase shift = ⅔
D. amplitude = 2, period = 2π/3, phase shift = 4⁄3
검증된 단계별 안내1
Identify the general form of the sine function: \(y = A \sin(Bx - C)\), where \(A\) is the amplitude, \(B\) affects the period, and \(C\) affects the phase shift.
From the given function \(y = 3 \sin(2x - 4)\), note that the amplitude \(A\) is the coefficient before the sine, which is 3.
Calculate the period using the formula \(\text{Period} = \frac{2\pi}{B}\). Here, \(B = 2\), so the period is \(\frac{2\pi}{2} = \pi\).
Find the phase shift using the formula \(\text{Phase shift} = \frac{C}{B}\). Since the function is \(\sin(2x - 4)\), rewrite the inside as \(2(x - 2)\), so the phase shift is \(\frac{4}{2} = 2\).
Match the values amplitude = 3, period = \(\pi\), and phase shift = 2 with the correct description in Column II, which corresponds to option B.
비슷한 문제에 대한 검증된 영상 답변:
이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
도움이 되었나요?
주요 개념
질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.
Amplitude of a Sine Function
Amplitude is the maximum value or height of the sine wave from its midline. For a function y = a sin(bx + c), the amplitude is the absolute value of 'a'. It determines how far the graph stretches vertically from the center line.
추천 영상:
5:05
Amplitude and Reflection of Sine and Cosine
Period of a Sine Function
The period is the length of one complete cycle of the sine wave. It is calculated as (2π) divided by the absolute value of the coefficient 'b' in y = a sin(bx + c). The period tells how frequently the wave repeats over the x-axis.
추천 영상:
5:33Period of Sine and Cosine Functions
Phase Shift of a Sine Function
Phase shift is the horizontal translation of the sine graph, determined by solving (bx + c) = 0 for x. It equals -c/b and indicates how far the graph shifts left or right from the origin. This shift affects where the wave starts on the x-axis.
추천 영상:
6:31Phase Shifts
관련 실천
교과서 질문
Identify the circular function that satisfies each description.
period is π; function is decreasing on the interval (0, π)
650
views
교과서 질문
Match each function with its graph in choices A–I. (One choice will not be used.)
y = -1 + cos x
A. <IMAGE> B. <IMAGE> C. <IMAGE>
D. <IMAGE> E. <IMAGE> F. <IMAGE>
G. <IMAGE> H. <IMAGE> I. <IMAGE>
864
views
교과서 질문
Match each function in Column I with the appropriate description in Column II.
I
y = -4 sin(3x - 2)
II
A. amplitude = 2, period = π/2, phase shift = ¾
B. amplitude = 3, period = π, phase shift = 2
C. amplitude = 4, period = 2π/3, phase shift = ⅔
D. amplitude = 2, period = 2π/3, phase shift = 4⁄3
743
views
교과서 질문
Graph each function over a one-period interval.
y = -2 tan (¼ x)
651
views
교과서 질문
Graph each function over a one-period interval.
y = cot (3x)
846
views