Question 928243
To make the equation look simpler, let's define
{{{x=cos(theta)}}} and {{{y=sin(theta)}}}
Now the equation looks less scary:
{{{y+x=2(y-x)}}}
and we can solve it for {{{y}}} (as a function of {{{x}}} , of course):
{{{y+x=2(y-x)}}}--->{{{y+x=2y-2x}}}--->{{{x+2x=2y-y}}}--->{{{3x=y}}}
Now, let's go back to {{{theta}}} :
{{{y=3x}}} means
{{{sin(theta)=3cos(theta)}}}--->{{{sin(theta)/cos(theta)=3}}}--->{{{tan(theta)=3}}}
Since tangent has a period of {{{180^o}}} ,
in the range {{{0^o<theta<360^o}}} there are two angles ( {{{180^o}}} apart) that have {{{tan(theta)=3}}} .
Their approximate measures are {{{theta=71.565^o}}} and {{{theta=251.565^o}}} .