Question

give a general formula for all the solutions. 7 sin θ - 5 = 2 sin θ select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. θ = (simplify your answer. type your answer(s) as an expression, using n as the variable, in the form a + bn where 0 ≤ a < 2π. type any angle measures in radians, using π as needed. use integers or fractions for any numbers in the expression. use a comma to separate answers as needed.) b. there is no solution.

Explanation:

Step1: Simplify the equation

$$\begin{align*} 7\sin\theta - 5&=2\sin\theta\\ 7\sin\theta-2\sin\theta&=5\\ 5\sin\theta&=5\\ \sin\theta& = 1 \end{align*}$$

Step2: Find the general solution

We know that the general solution of $\sin\theta = 1$ is $\theta=\frac{\pi}{2}+ 2n\pi$, where $n\in\mathbb{Z}$ (because the sine function has a period of $2\pi$ and $\sin\frac{\pi}{2}=1$).

Answer:

A. $\theta=\frac{\pi}{2}+2n\pi$