Question

How do you find the exact value of `2cosx+1=0` in the interval `0<=x<360`?

Answer 1

`x=120^@" or "x=240^@`

Explanation:

`"isolate " cosx^@`

`"subtract 1 from both sides"`

`rArr2cosx^@=-1`

`"divide both sides by 2"`

`rArrcosx^@=-1/2`

`rArrx=cos^-1(1/2)=60^@larrcolor(red)" related acute angle"`

`"since "cosx^@<0" then x in second / third quadrant"`

`rArrx=(180-60)=120^@larrcolor(red)" in second quadrant"`

`rArrx=(180+60)=240^@larrcolor(red)" in third quadrant"`

`rArrx=120^@" or " x=240^@to0<= x< 360`