How do I solve cos(x/2)=sqrt(2)/2 with a domain of [-720º,360º)?

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Answer 1 · 2018-04-12T11:40:53

$color(blue)(-630^@,-90^@,90^@)$

$cos(x/2)=sqrt(2)/2$

$x/2=arccos(cos(x/2))=arccos(sqrt(2)/2)$

$=>x/2=45^@, 315^@$

$x/2=45^@+n360^@=>x=90^@+n720^@$

$x/2=315^@+n360^@=>x=630^@+n720^@$

For:

$n in ZZ$

We now use:

$x=90^@+n720^@ and x=630^@+n720^@$

with integer n values to find angles in the interval:

$[-720^@,360^@)$

$n=0-> 90^@, 630^@$

$n=-1 -> -630^@, -90^@$
$n=-2 -> -1350^@, -810^@$

So only the values:

$color(blue)(-630^@,-90^@,90^@)$