College Algebra & Trigonometry, 2018a

10.2. DOUBLE-ANGLE IDENTITIES 449
(cos(α − β), sin(α − β))
α − β
(1, 0)
Since the the second diagram is created by rotating the lines and points from the
first diagram, the distance between the points (cos α, sin α) and (cos β,sin β) in the
first diagram is the same as the distance between (cos(α − β), sin(α − β)) and the
point (1, 0) in the second diagram.
(cosα, sin α)
d
(cos(α − β), sin(α − β))
α − β
(cos β,sin β)
d
α
β
(1, 0)
α − β
(1, 0)
In the diagram above the length of d in each picture is the same.