Solve the following equations on the interval 0 is less than or equal to beta and beta is less that 2 pi? 2cos^2x+cosx=0
1 Answer
Feb 8, 2018
Explanation:
#2cos^2x+cosx=0#
#"take out a "color(blue)"common factor of cosx"#
#rArrcosx(2cosx+1)=0#
#"equate each factor to zero and solve for x"#
#cosx=0rArrx=pi/2" or "x=(3pi)/2#
#2cosx+1=0rArrcosx=-1/2#
#"hence x is in the second/third quadrants"#
#rArrx=cos^-1(1/2)=pi/3larrcolor(red)"related acute angle"#
#rArrx=(pi-pi/3)=(2pi)/3larrcolor(blue)"second quadrant"#
#"or "x=(pi+pi/3)=(4pi)/3larrcolor(blue)"third quadrant"#
#"putting the solutions together"#
#x=pi/2,(2pi)/3,(4pi)/3,(3pi)/2#