[0/1 Points] DETAILS PREVIOUS ANSWERS SPRECALC7 7.5.007. Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms 4sin(2theta)-7sin(theta)=0

Factor the equation: Factor the equation to find common terms. We can factor sin(θ) out of the equation: sin(θ)(4sin(θ) - 7) = 0Set equal to zero: Set each factor equal to zero to find the solutions. sin(θ) = 0 and 4sin(θ) - 7 = 0Solve sin(θ) = 0: Solve the first equation sin(θ) = 0. The solutions to sin(θ) = 0 are θ = kπ, where k is any integer.Solve 4sin(θ) - 7 = 0: Solve the second equation 4sin(θ) - 7 = 0. First, add 7 to both sides: 4sin(θ) = 7 Then, divide both sides by 4: sin(θ) = 7/4 However, since the sine function has a range of [-1, 1], there are no solutions to sin(θ) = 7/4. This is not a valid solution.

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$4\sin(2\theta)-7\sin(\theta)=0$

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Algebra 2

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4\sin(2\theta)-7\sin(\theta)=0

Factor the equation: Factor the equation to find common terms. $\newline$ We can factor $\sin(\theta)$ out of the equation: $\newline$ $\sin(\theta)(4\sin(\theta) - 7) = 0$
Set equal to zero: Set each factor equal to zero to find the solutions. $\newline$ $\sin(\theta) = 0$ and $4\sin(\theta) - 7 = 0$
Solve $\sin(\theta) = 0$ : Solve the first equation $\sin(\theta) = 0$ . The solutions to $\sin(\theta) = 0$ are $\theta = k\pi$ , where $k$ is any integer.
Solve $4\sin(\theta) - 7 = 0$ : Solve the second equation $4\sin(\theta) - 7 = 0$ . $\newline$ First, add $7$ to both sides: $\newline$ $4\sin(\theta) = 7$ $\newline$ Then, divide both sides by $4$ : $\newline$ $\sin(\theta) = \frac{7}{4}$ $\newline$ However, since the sine function has a range of $[-1, 1]$ , there are no solutions to $\sin(\theta) = \frac{7}{4}$ . This is not a valid solution.