Question

Is anyone available to assist with a pre-calc problem? Thanks

Answer 1

STEP - BY - STEP EXPLANATION

What to find?

The values of x.

Given:

`sin^2x+sinx=0`

Step 1

Factorize sinx.

`sinx(sinx+1)=0`

Step 2

Equate each to zero.

`\begin{gathered} sinx=0 \\ \\ sinx+1=0 \\ \Rightarrow sinx=-1 \end{gathered}`
`\begin{gathered} sinx=0 \\ \Rightarrow x=2\pi n \\ \Rightarrow x=0,\text{ 2}\pi \end{gathered}`
`\begin{gathered} sinx=-1 \\ \Rightarrow x=(3\pi)/(2)+2\pi n \\ \\ x=(3\pi)/(2) \end{gathered}`

ANSWER

`x=0,\text{ 2}\pi,\text{ }(3\pi)/(2)`