11. The general solutions to the trigonometric equation can be written in the form, - \( x=\frac{a \pi}{b}+n 2 \pi, n \varepsilon I \) - \( x=\frac{c \pi}{b}+n 2 \pi, n \varepsilon I \) - \( x=d \pi+n 2 \pi, n \varepsilon I \) Record the values of \( a, b, c \) and \( d \) as a four digit number, in that order. Your answer:
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To solve the trigonometric equation, we need to determine the values of \( a \), \( b \), \( c \), and \( d \) from the general solutions provided. Let's consider a standard trigonometric equation like \( \sin(x) = 0 \). For \( \sin(x) = 0 \), the solutions are \( x = n\pi \), where \( n \in \mathbb{Z} \). In comparing this to the provided forms: - For \( x = n\pi \), we can write it as \( x = d\pi + n 2\pi \), where \( d = 0 \). - In \( x=\frac{a \pi}{b}+n 2 \pi \) and \( x=\frac{c \pi}{b}+n 2 \pi \), we can assume \( a = 0 \) and \( b = 1 \) for the simplest rational form. Thus, \( a = 0 \), \( b = 1 \), \( c = 0 \), and \( d = 0 \). Recording these values as a four-digit number: **0000**.