?

Log in

No account? Create an account
Eyes

Yay

2sin−1(sqrt(2+(1−P)cos(φ1+φ2)−(1+P)cos(φ1φ2))/2)

where P=cos(θ1θ2).

Phew.

Edit:

cos−1(cosφDcos2θA−cosφSsin2θA)

where φS=φ1+φ2, φD=φ1φ2 and θA=(θ2θ1)/2.

Comments

Okay, explain how you did it.

Just a bunch of trigonometric identities applied... XD

The second formula comes from the (forgotten) fact that the inner product of two vectors sharing the same origin equals to the cosine of the angle between them.  Much easier/simpler than the brute-force approach I took to derive the first formula (which involves getting the distance between the two points). :D

YOU SAID IT