College Trigonometry, 2011a

732 Foundations of Trigonometry
Theorem 10.3 gives us what we need to describe the position of an object traveling in a circular
path of radius r with constant angular velocity ω. Suppose that at time t, the object has swept
out an angle measuring θ radians. If we assume that the object is at the point (r, 0) when t =0,
the angle θ is in standard position. By definition, ω = θ t
which we rewrite as θ = ωt. According
to Theorem 10.3, the location of the object Q(x, y) on the circle is found using the equations
x = r cos(θ) =r cos(ωt) andy = r sin(θ) =r sin(ωt). Hence, at time t, the object is at the point
(r cos(ωt),rsin(ωt)). We have just argued the following.
Equation 10.3. Suppose an object is traveling in a circular path of radius r centered at the
origin with constant angular velocity ω. Ift = 0 corresponds to the point (r, 0), then the x and
y coordinates of the object are functions of t and are given by x = r cos(ωt) andy = r sin(ωt).
Here, ω>0 indicates a counter-clockwise direction and ω