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Unformatted text preview: wo examples of what are commonly thought of as angles are Q
P An angle with vertex P . An angle with vertex Q. However, the two ﬁgures below also depict angles - albeit these are, in some sense, extreme cases.
In the ﬁrst case, the two rays are directly opposite each other forming what is known as a straight
angle; in the second, the rays are identical so the ‘angle’ is indistinguishable from the ray itself.
P A straight angle.
The measure of an angle is a number which indicates the amount of rotation that separates the
rays of the angle. There is one immediate problem with this, as pictured below. 594 Foundations of Trigonometry Which amount of rotation are we attempting to quantify? What we have just discovered is that
we have at least two angles described by this diagram.1 Clearly these two angles have diﬀerent
measures because one appears to represent a larger rotation than the other, so we must label them
diﬀerently. In this book, we use lower case Greek letters such as α (alpha), β (beta), γ (gamma)
and θ (thet...
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