X 796 115 applications of trigonometry graphs of polar

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Unformatted text preview: this case reduces to 6 cos(φ) = 0. 3 5 11.1 Applications of Sinusoids 755 It is possible, though beyond the scope of this course, to model the effects of friction and other external forces acting on the system.15 While we may not have the Physics and Calculus background to derive equations of motion for these scenarios, we can certainly analyze them. We examine three cases in the following example. Example 11.1.4. √ 1. Write x(t) = 5e−t/5 cos(t) + 5e−t/5 3 sin(t) in the form x(t) = A(t) sin(ωt + φ). Graph x(t) using a graphing utility. √ √ 2. Write x(t) = (t + 3) 2 cos(2t) + (t + 3) 2 sin(2t) in the form x(t) = A(t) sin(ωt + φ). Graph x(t) using a graphing utility. 3. Find the period of x(t) = 5 sin(6t) − 5 sin (8t). Graph x(t) using a graphing utility. Solution. √ 1. We start rewriting x(t) = 5e−t/5 cos(t√+ 5e−t/5 3 sin(t) by factoring out 5e−t/5 from both ) terms to get x(t) = 5e−t/5 cos(t) + 3 sin(t) . We convert what’s left in parentheses to the required form using the formulas introduced in Exe...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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