Question

Use Euler's relation to with the following functions in the form x(t) = Acos(ω₀t + ϕ)

x(t) = 3cos(2t) + sin(2t)

Answer 1

To use Euler's relation with the given functions, rewrite the equation using Euler's formula: x(t) = A(cos(ω₀t) + i sin(ω₀t)). For example, if we have x(t) = 3cos(2t) + sin(2t), rewrite it as x(t) = 3(cos(2t) + i sin(2t)).

Step-by-step explanation:

To use Euler's relation with the given functions in the form x(t) = Acos(ω₀t + ϕ), we can rewrite the equation using Euler's formula: x(t) = A(cos(ω₀t) + i sin(ω₀t)).

For example, if we have x(t) = 3cos(2t) + sin(2t), we can rewrite it as x(t) = 3(cos(2t) + i sin(2t)).

This allows us to express the function in terms of the complex exponential function, which can be useful in certain mathematical calculations.