Question 1022987
.
2sin^2 theta plus 3sin theta = -1
Solve for the given domain:
0greater than or equal to theta greater than or equal to 2pi
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{{{2*sin^2(theta) + 3*sin(theta)}}} = {{{-1}}},

{{{2*sin^2(theta) + 3*sin(theta) + 1}}} = {{{0}}}.

Factor left side:

(2*sin(theta) + 1)*(sin(theta) + 1) = 0,   --->

{{{2*sin(theta) + 1}}} = {{{0}}}  or  {{{sin(theta) + 1}}} = {{{0}}},  --->

{{{sin(theta)}}} = {{{-1/2}}}  or  {{{sin(theta)}}} = -1,  --->

Solutions:

1.    {{{theta}}} = {{{7*pi/6}}}  or  {{{theta}}} = {{{11*pi/6}}}

or

2.    {{{theta}}} = {{{3*pi/2}}}.
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