How do you find all solutions to $cos( x+pi/6)=-0.5$ on [0,2pi)?

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Answer 1 · 2016-04-11T08:46:51

$(13pi)/12 and (5pi)/12$ .

Cosine is negative for angles in the 2nd and the 3rd quadrants
$cos(pi+-a)=-cos a$ ..

From the given equation,
$x+pi/6=arc cos (-1/2), pi+-arc cos(1/2)= pi+-pi/3$ .

$x= pi+-pi/3-pi/4$
$=pi(1+1/3-1/4) and pi(1-1/3-1/4)$
$=(13pi)/12 and (5pi)/12$ .

How do you find all solutions to cos( x+pi/6)=-0.5cos( x+pi/6)=-0.5 on [0,2pi)?