How do you find all solutions of the equation sin^2x+sinx=0?

1 Answer
Luca F.
Jun 9, 2015

S={x|x=kpivvx=-3/2pi+2kpi ^^kinZZ}

Explanation:

sin^2x+sinx=0
can be rewritten:
sinx(sinx+1)=0
So we can state that sinx=0 or sinx=-1 because multiplying two numbers can result zero if and only if one of the two is zero.
So let's solve the two parts of the equation:
1. sin(x)=0
It is basically x=kpi where kinZZ
2. sin(x)=-1
It is basically x=-3/2pi+2kpi where kinZZ

So the solutions are:
S={x|x=kpivvx=-3/2pi+2kpi ^^kinZZ}

Related questions
See all questions in Solving Trigonometric Equations
Impact of this question
12158 views around the world
You can reuse this answer
Creative Commons License