Unformatted text preview: r, 0), it can be shown the position of the object is given
by x = r cos(ω (t − t0 )) and y = r sin(ω (t − t0 )).
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You may have been exposed to this in High School. 628 Foundations of Trigonometry
y
c P (a, b)
c θ b x
c θ
a According to the Pythagorean Theorem, a2 + b2 = c2 , so that the point P (a, b) lies on a circle of
b
radius c. Theorem 10.3 tells us that cos(θ) = a and sin(θ) = c , so we have determined the cosine
c
and sine of θ in terms of the lengths of the sides of the right triangle. Thus we have the following
theorem.
Theorem 10.4. Suppose θ is an acute angle residing in a right triangle. If the length of the side
adjacent to θ is a, the length of the side opposite θ is b, and the length of the hypotenuse is c,
a
b
then cos(θ) = and sin(θ) = .
c
c
Example 10.2.8. Find the measure of the missing angle and the lengths of the missing sides of: 30◦
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Solution. The ﬁrst and easiest task is to ﬁnd the measure of the missing angle. Since the sum of
angles of a triangle is 180◦ , we kn...
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 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

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