How to solve the equation? 2cosθ/2+1=0 0<θ<2π

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Answer 1 · 2018-03-28T06:55:54

$theta=(4pi)/3$

We are given

$2cos(theta/2)+1=0$

$rArr2cos(theta/2)=-1$

$rArrcos(theta/2)=-1/2$

$rArrtheta/2=arccos(-1/2)$

This will return 2 possible values for $theta/2$ . They are:

$rArrtheta/2=(2pi)/3, (4pi)/3$

$rArrtheta=(4pi)/3, (8pi)/3$

However, the question states that $0$ $<$ $theta<2pi$

So our only valid solution is $theta=(4pi)/3$