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Ch. 1 - Functions
Briggs - Calculus: Early Transcendentals 3rd Edition
Briggs3rd EditionCalculus: Early TranscendentalsISBN: 9780136847243당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Briggs 3rd EditionCh. 1 - Functions문제 99
1장, 문제 99

Identify the amplitude and period of the following functions.
q(x)=3.6cos(πx24)q\(\left\)(x\(\right\))=3.6\(\cos\[\left\)(\(\frac{\pi x}{24}\]\right\))

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The function given is q(x) = 3.6 \(\cos\[\left\)(\(\frac{\pi x}{24}\]\right\)). This is a cosine function of the form a \(\cos\)(bx), where 'a' is the amplitude and 'b' affects the period.
Identify the amplitude: In the function q(x) = 3.6 \(\cos\[\left\)(\(\frac{\pi x}{24}\]\right\)), the coefficient 'a' in front of the cosine function is 3.6. Therefore, the amplitude is 3.6.
Determine the period: The period of a cosine function a \(\cos\)(bx) is given by \(\frac{2\pi}{b}\).
In the function q(x) = 3.6 \(\cos\[\left\)(\(\frac{\pi x}{24}\]\right\)), the value of 'b' is \(\frac{\pi}{24}\).
Calculate the period using the formula: Substitute b = \(\frac{\pi}{24}\) into the period formula \(\frac{2\pi}{b}\) to find the period of the function.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Amplitude

Amplitude refers to the maximum distance a wave reaches from its central position, which in the context of a cosine function is the coefficient in front of the cosine term. For the function q(x) = 3.6cos(πx/24), the amplitude is 3.6, indicating that the function oscillates between 3.6 and -3.6.
추천 영상:
가이드 코스
3:40
Introduction to Cotangent Graph Example 1

Period

The period of a function describes the length of one complete cycle of the wave. For a cosine function of the form cos(kx), the period can be calculated using the formula P = 2π/k. In this case, k is π/24, leading to a period of P = 2π/(π/24) = 48, meaning the function completes one full cycle every 48 units along the x-axis.
추천 영상:
가이드 코스
5:43
Introduction to Tangent Graph

Cosine Function

The cosine function is a fundamental trigonometric function that describes the relationship between the angle and the lengths of the sides of a right triangle. It is periodic, oscillating between -1 and 1, and is often used to model wave-like phenomena. In the given function, the cosine term dictates the shape and behavior of the wave, influenced by its amplitude and period.
추천 영상:
가이드 코스
5:53
Graph of Sine and Cosine Function
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