Question 1009491
.
Solve {{{sin(2theta)}}} + {{{sin(theta)))}}} = {{{0}}}
-------------------------------------------------------

<pre>
The double-argument formula says that {{{sin(2theta)}}} = {{{2*sin(theta)*cos(theta)}}}. 

(See, for example, the lesson <A HREF=http://www.algebra.com/algebra/homework/Trigonometry-basics/Trigonometric-functions-of-multiply-argument.lesson>Trigonometric functions of multiply argument</A> in this site).


Substitute it into the original equation, and you will get

{{{2*sin(theta)*cos(theta)}}} + {{{sin(theta)}}} = {{{0}}}.

Now factor it:

{{{sin(theta)}}}.{{{(2cos(theta)+1)}}} = {{{0}}}.

Thus you get two equations:

1) {{{sin(theta)}}} = {{{0}}},  which has two solutions  {{{theta}}} = {{{0}}} and {{{pi}}} in the given interval for {{{theta}}}.


2) {{{2cos(theta)+1}}} = {{{0}}},  or {{{cos(theta)}}} = {{{-1/2}}}, which has two solutions {{{theta}}} = {{{2pi/3}}} and {{{4pi/3}}}.

<U>Answer</U>. The solutions are {{{theta}}} = {{{0}}}, {{{2pi/3}}}, {{{pi}}} and {{{4pi/3}}}.
</pre>