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Given two signals: x(t) = 4cos(2t-30°) and y(t) = 3sin(2t+60°) what is the amplitude (M) of the sum of these signals in cosine form x(t) + y(t) = Mcos(2t+q)? Answer: Amplitude M equals: A 7 B 5 Note that, since sin (0+π/2) = cos(0) D 4/3 3sin(2t+60) = 3 cos(2t-30) thus, 4 cos(2t-30) + 3 sin(2t+60) = 4cos(2t-30)+3 cos (2t-30) = 7 cos(2t-30) Hence, (a) M = 7 and (b) qp=-30°. E. None of these

Given two signals: x(t) = 4cos(2t-30°) and y(t) = 3sin(2t+60°) what is the amplitude (M) of the sum of these signals in cosine form x(t) + y(t) = Mcos(2t+q)? Answer: Amplitude M equals: A 7 B 5 Note that, since sin (0+π/2) = cos(0) D 4/3 3sin(2t+60) = 3 cos(2t-30) thus, 4 cos(2t-30) + 3 sin(2t+60) = 4cos(2t-30)+3 cos (2t-30) = 7 cos(2t-30) Hence, (a) M = 7 and (b) qp=-30°. E. None of these

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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Given two signals: \( x(t) = 4\cos(2t - 30^\circ) \) and \( y(t) = 3\sin(2t + 60^\circ) \) What is the amplitude (M) of the sum of these signals in cosine form \( x(t) + y(t) = M\cos(2t + \varphi) \)? **Answer: Amplitude M equals:** - A: 7 - B: 5 - C: 1 - D: 4/3 - E: None of these Note that, since \( \sin(\theta + \pi/2) = \cos(\theta) \), \( 3\sin(2t + 60) = 3\cos(2t - 30) \) Thus, \[4\cos(2t - 30) + 3\sin(2t + 60) = 4\cos(2t - 30) + 3\cos(2t - 30) = 7\cos(2t - 30)\] Hence, (a) \( M = 7 \) and (b) \( \varphi = -30^\circ \).
Transcribed Image Text:Given two signals: \( x(t) = 4\cos(2t - 30^\circ) \) and \( y(t) = 3\sin(2t + 60^\circ) \) What is the amplitude (M) of the sum of these signals in cosine form \( x(t) + y(t) = M\cos(2t + \varphi) \)? **Answer: Amplitude M equals:** - A: 7 - B: 5 - C: 1 - D: 4/3 - E: None of these Note that, since \( \sin(\theta + \pi/2) = \cos(\theta) \), \( 3\sin(2t + 60) = 3\cos(2t - 30) \) Thus, \[4\cos(2t - 30) + 3\sin(2t + 60) = 4\cos(2t - 30) + 3\cos(2t - 30) = 7\cos(2t - 30)\] Hence, (a) \( M = 7 \) and (b) \( \varphi = -30^\circ \).
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