How do you solve $cos(2x-pi/2)=1$ ?

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How do you solve $cos(2x-pi/2)=1$ ?

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Answer 1 · 2016-08-20T03:29:26

$pi/4 + 2kpi$
$(5pi)/4 + 2kpi$

Explanation:

Trig unit circle -->
$cos (2x - pi/2) = 1$
There are 2 solution arcs:
a. $(2x - pi/2) = 0$
$2x = pi/2$
$x = pi/4$
b. $2x - pi/2 = 2pi$ -->
$2x = 2pi + pi/2 = 5pi/2$
$x = (5pi)/4$
General answers:
$x = pi/4 + 2kpi$
$x = (5pi)/4 + 2kpi$

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