Question

Can someone help me with Problem Set 1: 1B-13

Answer 1

The question asks us to solve for cos(Θ1−Θ2), but the answer in the supplemental packet solves for cos(Θ2−Θ1). Is this a mistake?

Answer 2

cos(-x) = cos(x) so their switching theta1 and theta2 does not change the answer.
(Though it would be nice if they were consistent, so as not to introduce confusion)

Answer 3

Here are more details on their derivation of the cos of a difference of two angles.

First, they define a unit length vector with its tail at the origin and its head lying on the unit circle. Based on this definition, we know its i and j components


we thus have two unit vectors
\[ \vec{u_1}= < \cos \theta_1 , \sin \theta_1> \\
\vec{u_2}= < \cos \theta_2 , \sin \theta_2> \]