8. 0.68/1 points details my notes larpcalclim4hs 5.3.019.mi.sa. this question has several parts that must be…

8. 0.68/1 points details my notes larpcalclim4hs 5.3.019.mi.sa. this question has several parts that must be completed sequentially. if you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. tutorial exercise solve the equation. (enter your answers as a comma - separated list. use n as an integer constant. enter your response in radians.) sin x(sin x + 1)=0 step 1 set each factor equal to zero. sin(x) sin(x)=0 or sin x + 1 = 0 therefore, sin(x) sin(x)=0 or sin x=-1 -1. step 2 as sin x has a period of 2π, there are infinitely many solutions outside the range 0 < x < 2π. in fact, any angle that is coterminal coterminal with x = 0 and x = 2π 3π/2 will be a solution of the origi step 3 therefore, the solutions of the original equation are the following. (enter your answers as a comma - separated list. use n as an integer constant. enter your response in radians.) x = submit skip (you cannot come back)

8. 0.68/1 points details my notes larpcalclim4hs 5.3.019.mi.sa. this question has several parts that must be completed sequentially. if you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. tutorial exercise solve the equation. (enter your answers as a comma - separated list. use n as an integer constant. enter your response in radians.) sin x(sin x + 1)=0 step 1 set each factor equal to zero. sin(x) sin(x)=0 or sin x + 1 = 0 therefore, sin(x) sin(x)=0 or sin x=-1 -1. step 2 as sin x has a period of 2π, there are infinitely many solutions outside the range 0 < x < 2π. in fact, any angle that is coterminal coterminal with x = 0 and x = 2π 3π/2 will be a solution of the origi step 3 therefore, the solutions of the original equation are the following. (enter your answers as a comma - separated list. use n as an integer constant. enter your response in radians.) x = submit skip (you cannot come back)

Answer

Explanation:

Step1: Set factors to zero

We have $\sin x(\sin x + 1)=0$. By the zero - product property, if $ab = 0$, then $a = 0$ or $b = 0$. So $\sin x=0$ or $\sin x+1 = 0$, which simplifies to $\sin x=0$ or $\sin x=-1$.

Step2: Recall the period of sine function

The sine function $y = \sin x$ has a period of $2\pi$. The solutions of $\sin x = 0$ are $x = n\pi$, where $n\in\mathbb{Z}$ (because $\sin(0)=0,\sin(\pi)=0$ and due to the periodicity). The solutions of $\sin x=-1$ are $x=\frac{3\pi}{2}+2n\pi$, where $n\in\mathbb{Z}$ (since $\sin(\frac{3\pi}{2})=-1$ and considering the period).

Step3: Combine the solutions

Combining the two sets of solutions, the solutions of the equation $\sin x(\sin x + 1)=0$ are $x = n\pi,\frac{3\pi}{2}+2n\pi$, $n\in\mathbb{Z}$.

Answer:

$n\pi,\frac{3\pi}{2}+2n\pi$