How do you find all solutions to the equation $cos 2 x = \frac{1}{2}$ $cos2x=1/2$ ?

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How do you find all solutions to the equation $cos 2 x = \frac{1}{2}$ $cos2x=1/2$ ?

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Answer 1 · 2017-02-09T17:15:50

$x = \frac{π}{6} + n π$ $x = pi/6 + npi$

Explanation:

cos x is a periodic function, so you expect many solutions. If $cos 2 x = \frac{1}{2}$ $cos2x = 1/2$ , which is cos (pi/3) so $2 x = \frac{π}{3} + 2 n π$ $2x = pi/3 + 2npi$ or $x = \frac{π}{6} + n π$ $x = pi/6 + npi$

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How do you find all solutions to the equation $cos 2 x = \frac{1}{2}$ $cos2x=1/2$ ?

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How do you find all solutions to the equation $cos 2 x = \frac{1}{2}$ $cos2x=1/2$ ?