solve-for-0-2pi-the-equation-cos-pi-3-1-2-

Question Number 49064 by Rio Michael last updated on 02/Dec/18

s o l v e f o r 0 ° ⩽ θ ⩽ 2 π t h e e q u a t i o n

c o s (θ + \frac{π}{3}) = \frac{1}{2}

Answered by hknkrc46 last updated on 02/Dec/18

\cos (θ + \frac{π}{3}) = \cos (\frac{π}{3})

θ + \frac{π}{3} = \frac{π}{3} + 2 π k \lor - (θ + \frac{π}{3}) = \frac{π}{3} + 2 π k (k \in Z)

θ = 2 π k \lor - θ - \frac{π}{3} = \frac{π}{3} + 2 π k (k \in Z)

θ = 2 π k \lor - θ = \frac{2 π}{3} + 2 π k (k \in Z)

θ = 2 π k \lor θ = - \frac{2 π}{3} - 2 π k (k \in Z)

θ = 2 π k \lor θ = - \frac{2 π}{3} + 2 π k (k \in Z) ★

θ = 2 π k \land k = 0 \Rightarrow θ = 0

θ = 2 π k \land k = 1 \Rightarrow θ = 2 π

θ = - \frac{2 π}{3} + 2 π k \land k = 1 \Rightarrow θ = \frac{4 π}{3}

{0, \frac{4 π}{3}, 2 π}

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