How do I solve for x in degrees given cos² x = cos x?

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Answer 1 · 2018-02-21T01:11:45

#x=90°+180°n# and #x=360°n# where n is any integer.

Move everything to one side (we'll generally do this when solving trigonometric equations involving squared terms).

#cos^2(x)-cos(x)=0#

This resembles a quadratic. We can factor out #cos(x)#, as it occurs in both terms.

#cos(x)[cos(x)-1]=0#

We now have two separate equations to solve:

#cos(x)=0#

and

#cos(x)-1=0#

For #cos(x)=0#:

#x=pi/2+npi# where n is any integer.

Converting to degrees means multiplying each term in this answer by #(180°)/pi#

#x=(cancelpi/2)((180°)/cancelpi)+(ncancelpi)((180°)/cancelpi)#

#x=90°+180°n#

For #cos(x)-1=0#

#cos(x)=1#

#x=2npi# where n is any integer.

Convert to degrees:

#x=2ncancelpi*((180°)/cancelpi)#
#x=360°n#