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Unformatted text preview: .1.1, we introduced circular motion and derived a formula which describes the linear
velocity of an object moving on a circular path at a constant angular velocity. One of the goals of
this section is describe the position of such an object. To that end, consider an angle θ in standard
position and let P denote the point where the terminal side of θ intersects the Unit Circle. By
associating a point P with an angle θ, we are assigning a position P on the Unit Circle to each
angle θ. The x-coordinate of P is called the cosine of θ, written cos(θ), while the y -coordinate of
P is called the sine of θ, written sin(θ).1 The reader is encouraged to verify that the rules by which
we match an angle with its cosine and sine do, in fact, satisfy the deﬁnition of function. That is,
for each angle θ, there is only one associated value of cos(θ) and only one associated value of sin(θ).
y y 1 1 P (cos(θ), sin(θ))
1 x 1 x Example 10.2.1. Find the cosine and sine of the following angles.
1. θ = 270◦ 2....
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