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

#x=pi/2,(2pi)/3,(4pi)/3,(3pi)/2#

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#