solve for 0°≤ θ ≤ 360° the equation cos(θ + (π/3))= (1/2)


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Question Number 36092 by Rio Mike last updated on 28/May/18

$solve for 0 ° ⩽ θ ⩽ 360 ° the equation$ $\cos (θ + \frac{π}{3}) = \frac{1}{2}$
Commented by abdo mathsup 649 cc last updated on 30/May/18

$(e) \Leftrightarrow c o s (θ + \frac{π}{3}) = c o s (\frac{π}{3}) \Leftrightarrow θ + \frac{π}{3} = \frac{π}{3} + 2 k π$ $o r θ + \frac{π}{3} = - \frac{π}{3} + 2 k π \Leftrightarrow θ = 2 k π o r$ $θ = - \frac{2 π}{3} + 2 k π (k \in Z)$ $c a s e 1 0 ⩽ 2 k π ⩽ 2 π \Rightarrow 0 ⩽ k ⩽ 1 \Rightarrow k = 0 o r k = 1$ $c a s e 2 0 ⩽ - \frac{2 π}{3} + 2 k π ⩽ 2 π \Rightarrow$ $0 ⩽ - \frac{2}{3} + 2 k ⩽ 2 \Rightarrow 0 ⩽ - \frac{1}{3} + k ⩽ 1 \Rightarrow$ $\frac{1}{3} ⩽ k ⩽ \frac{4}{3} \Rightarrow k = 1 s o t h e s o l u t i o n f o r t h i s$ $e q u a t i o n a r e 0, 2 π, \frac{4 π}{3} .$
	Answered by Joel579 last updated on 28/May/18

	$\cos (θ + \frac{π}{3}) = \cos (\frac{π}{3})$ $θ + \frac{π}{3} = \frac{π}{3}$ $θ = 0$ $\cos (θ + \frac{π}{3}) = \cos (\frac{5 π}{3})$ $θ + \frac{π}{3} = \frac{5 π}{3}$ $θ = \frac{4 π}{3}$
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