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
Sam F.
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.

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