Cos

an angle of 234 degrees is in the  3rd quadrant,so the cosine is negative.     270  - 234  = 36.

So cos 234  =    -  (cos 36)

What is cos of 234 degrees ?

cos234° = - 0.587785252292

Q3->Q1=(x-180)º= (234-180)º=54º

cosine<0 in Q3

cos234º=-cos54º