Question 830491
Find all positive vales of theta less than 360degrees that satisfy the equation costheta=2+3cos2theta. Express your answers to the nearest ten minutes or nearest tenth of a degree.
***
(0<theta<360)
{{{cos(theta)=2+3cos(2theta)}}}
{{{cos(theta)=2+3(2cos^2(theta)-1)}}}
{{{cos(theta)=2+6cos^2(theta)-3)}}}
{{{6cos^2(theta)-cos(theta)-1=0)}}}
{{{(3cos(theta)+1)(2cos(theta)-1)=0)}}}
..
{{{(3cos(theta)+1)=0}}}
{{{cos(theta)=-1/3}}}
theta=109.5&#730;, 250.5&#730;(in quadrants II and III in which cos<0)
or
{{{(2cos(theta)-1)=0)}}}
{{{cos(theta)=1/2}}}
theta=60&#730;,300&#730;(in quadrants I and IV in which cos>0)