-How do you know what quadrant ( x + v) is in?
Please note that if I apply the formula of addition of the cosine function, I get:
cos(2v)=cos(v +v)= (cos v)^2 - (sin v)^2 =2 (cos(v))^2 - 1.
I substitute your numerical data and I get:
cos(2v) = 2 * (1/16) -1= 1/8 -1 = -7/8
furthermore, we have:
x= arcsin(2/3)= 138.19 degrees
v = arccos(-1/4) = 255.52
so x+v = 393.71 degrees then x+v belongs to the I quadrant since it is > 360 degrees and it is < 450 degrees
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