How do I solve the following equation? The answers that I came up with are wrong

solve the given equation:
sintheta(2sintheta+1)=0

1 Answer
Feb 9, 2018

In the interval [0,2pi), theta={0,pi, (5pi)/6, (7pi)/6}

Explanation:

There are two factors in your equation, basically sintheta xx (2sintheta + 1). If their product is zero, then one or both factors must be equal to zero as well (zero product property). Set each factor equal to zero and solve:

sintheta=0

sintheta is zero at 0 and pi (look at your unit circle)

2sintheta + 1=0
2sintheta =-1
sintheta =-1/2

sintheta -1/2 at (5pi)/6 and (7pi)/6 (again, look at your unit circle)

If you are looking for a general solution, you would add pin to 0 and 2pin to (5pi)/6 and (7pi)/6

Hope this helps.