Processing Math: Done

From Förberedande kurs i matematik 1

With the help of the Pythagorean identity, we can express cosv in terms of sinv,

cos2v+sin2v=1cosv=1−sin2v.

In addition, we know that the angle v lies between −2 and 2, i.e. either in the first or fourth quadrant, where angles always have a positive x-coordinate (cosine value); thus, we can conclude that

cosv=1−sin2v=1−a2.