Question 743932
Find all (theta) in the interval [0,2pi] satisfying
a) 2sin^2(theta) + sin(theta) = 1
{{{2sin^2(x)+sin(x)=1}}}
{{{2sin^2(x)+sin(x)-1=0}}}
{{{(2sin(x)-1)(sin(x)+1)=0}}}
2sin(x)-1=0
sin(x)=1/2
x=π/6, 5π/6
or
sin(x)+1=0
sin(x)=-1
x=3π/2
..
b) 5cos)theta) + 2cos(theta + pi) + 3sin(pi/2 - (theta)) = 3
{{{5cos(x)+2cos(x+pi)+3sin(pi/2-x)=3}}}
{{{5cos(x)-2cos(x)+3cos(x)=3}}}
6cos(x)=3
cos(x)=3/6=1/2
x=π/3, 5π/3