Stitz-Zeager_College_Algebra_e-book

Solution 1 the key to this problem is to use the

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Unformatted text preview: al side of an angle θ (plotted in standard position) which lies on the circle of radius r, x2 + y 2 = r2 . Then: • sec(θ) = r = x x2 + y 2 , provided x = 0. x • csc(θ) = r = y x2 + y 2 , provided y = 0. y y , provided x = 0. x x • cot(θ) = , provided y = 0. y • tan(θ) = Example 10.3.4. 1. Suppose the terminal side of θ, when plotted in standard position, contains the point Q(3, −4). Find the values of the six circular functions of θ. 2. Suppose θ is a Quadrant IV angle with cot(θ) = −4. Find the values of the five remaining circular functions of θ. Solution. √ 1. Since x = 3 and y = −4, r = x2 + y 2 = (3)2 + (−4)2 = 25 = 5. Theorem 10.9 tells us cos(θ) = 3 , sin(θ) = − 4 , sec(θ) = 5 , csc(θ) = − 5 , tan(θ) = − 4 , and cot(θ) = − 3 . 5 5 3 4 3 4 644 Foundations of Trigonometry 2. In order to use Theorem 10.9, we need to find a point Q(x, y ) which lies on the terminal side of θ, when θ is plotted in standard position. We have that cot(θ) = −4 = x , and since θ is a y 4 Qu...
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