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Stitz-Zeager_College_Algebra_e-book

# Solution we begin with a straightforward application

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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 )). 12 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◦ 7 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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