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=\frac{3\pi}{2}+2\pi n \\ \\ x=\frac{3\pi}{2} \end{gathered}$

ANSWER

$x=0,\text{ 2}\pi,\text{ }\frac{3\pi}{2}$