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Solve and plot the sum of the following expressions given that: v₁ =3cos(2πf₁t) and v₂ =2cos(2πf₂ +π/2).

Find v₂ + v₁​

2 Answers

3 votes

1. Solve and plot the answer to the following expressions given that:

V₁ = 3cos (2πf₁t) and v₂ = 2cos (2πf₂t + π/2).

a. Find v₂ + V1.

b. Find V2 * V1.

c. Assume that f₂ = f₁ and find v₂ + V1.

d. Assume that f₂ = f₁ and find V2 * V1.

User Bogdan Kobylynskyi
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5 votes

Final answer:

The sum of v1 = 3cos(2πf1t) and v2 = 2cos(2πf2t + π/2) is calculated by converting v2 into a sine function due to the phase shift, but without specific frequency values, the exact analytical form of their sum cannot be determined.

Step-by-step explanation:

Solving the Sum of Two Trigonometric Expressions

Given the expressions v1 = 3cos(2πf1t) and v2 = 2cos(2πf2t + π/2), we want to find and plot the sum v1 + v2. To solve this, we first recognize that these are trigonometric functions of time with different frequencies and a phase shift in the case of v2.

Since v2 has a phase shift of π/2, it represents a sine function. Therefore, we can rewrite it as v2 = 2sin(2πf2t) because a cosine function shifted by π/2 is equivalent to a sine function. The sum of these two functions is not trivial and requires knowledge of trigonometric identities and possibly numerical methods or software to evaluate and plot, particularly if the frequencies f1 and f2 are not the same or do not have a simple ratio.

The sum v1 + v2 is a new trigonometric function that combines the effects of both individual functions, but without further information on the frequencies, the exact form of this sum cannot be determined analytically. If f1 = f2, then the sum will be easier to evaluate as it will involve trigonometric identities for summing cosines and sines with same frequencies but different phase shifts.

User Jonah Ruffer
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