This means we have a pair of vertical asymptotes to

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Unformatted text preview: ns, we get 3h = (h + 200) 3. The result is a linear equation for h, so we proceed to expand the right hand side and gather all the terms involving h to one side. √ 3h = (h + 200) 3 √ √ 3h = h 3 + 200 3 √ √ 3h − h 3 = 200 3 √ √ (3 − 3)h = 200 3 √ 200 3 √ ≈ 273.20 h= 3− 3 Hence, the tree is approximately 273 feet tall. As we did in Section 10.2.1, we may consider all six circular functions as functions of real numbers. At this stage, there are three equivalent ways to define the functions sec(t), csc(t), tan(t) and cot(t) for real numbers t. First, we could go through the formality of the wrapping function on page 604 and define these functions as the appropriate ratios of x and y coordinates of points on the Unit Circle; second, we could define them by associating the real number t with the angle θ = t radians so that the value of the trigonometric function of t coincides with that of θ; lastly, we could simply define them using the Reciprocal and Quotient Identities as combinations of the functions f (t) = cos(t) and g (t) = sin(t). Prese...
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