Question

I understand dot products, but this question is confusing me: Use the component form of dot product of two arbitrary vectors u and w to prove the trigonometric identity
cos (θ- β) = cos θ cos β + sin θ sin β

Answer 1

the component for of a vector A is written
\[A = A _{x}i + A _{y}j\]

A dot B = \[A _{x}B _{x} + A _{y}B _{y}\]

Can you do the rest?

Answer 2

I don't understand what A and what B are supposed to be in his particular problem

Answer 3

is this the one you wanted me to look at?

Answer 4

Yes it is

Answer 5

@amistre64

Answer 6

found it :)

Answer 7

Awesome, let me know if you have any ideas

Answer 8

A and B were generalities

what is the cos of an angle in dot product format?

Answer 9

The cos of the angle is usually used just to get one of the vectors in line with the other

Answer 10

\[cos(a)=\frac{\vec u\cdot \vec v}{|\vec u|~|\vec v|}\]

Answer 11

now, it looks like cos(a)cos(b) + sin(a)sin(b) is a dot product of: (cos(a),sin(a)) and (cos(b),sin(b))

Answer 12

cos(a-b) has a trig identity: it is equal to cos(a)cos(b) + sin(a)sin(b)

Answer 13

you are trying to prove this with a dotproduct method