How do you find all solutions if 0 ≤ θ < 2π for $cos 2x = sqrt2/2$ ?

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How do you find all solutions if 0 ≤ θ < 2π for $cos 2x = sqrt2/2$ ?

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Answer 1 · 2018-03-04T16:29:30

$pi/8; (7pi)/8$

Explanation:

$cos 2x = sqrt2/2$
Trig table and unit circle give 2 solutions:
$2x = +- pi/4$
a. $2x = pi/4$ -->
$x = pi/8$
b. $2x = - pi/4$ , or $2x = (7pi)/4$ --> (co-terminal)
$x = (7pi)/8$

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How do you find all solutions if 0 ≤ θ < 2π for $cos 2x = sqrt2/2$ ?

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How do you find all solutions if 0 ≤ θ < 2π for $cos 2x = sqrt2/2$ ?