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How do you solve $cos (2 t) = \frac{1}{2}$ $cos(2t)=1/2$ ?

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Nov 26, 2015

Since $cos (x) = \frac{1}{2}$ $cos(x)=1/2$ has the two solutions

$x = \frac{π}{3} + 2 k π$ $x=pi/3 + 2k\pi$
$x = \frac{5}{3} π + 2 k π$ $x=5/3 pi + 2k\pi$ ,

We simply need to substitute $x \to 2 t$ $x->2t$ , and solve for $t$ $t$ . So, we have

$2 t = \frac{π}{3} + 2 k π$ $2t=pi/3 + 2k\pi$
$2 t = \frac{5}{3} π + 2 k π$ $2t=5/3 pi + 2k\pi$

From which we have

$t = \frac{π}{6} + k π$ $t=pi/6 + k\pi$
$t = \frac{5}{6} π + k π$ $t=5/6 pi + k\pi$

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