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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