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^@)#