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This can be done using a graphing calculator or online graphing tool, or by hand by picking values for {eq}x It all depends on the value of B in the function f(x) = Acos(Bx + C) + D, where B is the coefficient of x. 8.5. The cosine function is a trigonometric function that's called periodic. {/eq}, so all four functions have a period of {eq}\dfrac{2\pi}{2}=\pi {/eq} look like compared to the graph of {eq}f(x) = \cos(3x) You see, the cosine function takes on many forms, expressed as: where A, B, C, and D are numbers, and the periods of these cosine functions differ. Record your score out of 28. Next, we plug B = 8 into the period formula. 3) How did the graphs of {eq}g(x), h(x), j(x) A ‘good’ … Continue reading → Suppose we want to find the period of the function g(x) = 3cos(8x + 1). Thus, in this example, the period would represent one cycle of the spring going from its highest, or most compressed position, to its lowest, or most stretched position, and then back to its highest position. {/eq}, shifted down one unit. })(window,document,'script','//www.google-analytics.com/analytics.js','ga'); {/eq} and {eq}D Without the plant on it, when you compress the spring 2 inches and let it go, its motion can be modeled by the following cosine function: where y is the displacement of the end of the spring, and x is the time in seconds. Read the lesson. Solving problems related to plane geometry especially circles and triangles can be easily solved using a calculator. This interval from x = 0 to x = 2π of the graph of f(x) = cos(x) is called the period of the function. Because of the nature of the cosine function, it can be used to model anything in the real world having simple harmonic motion, where simple harmonic motion is described as moving back and forth in a constant fashion with no friction involved. {/eq} units to the right if {eq}C<0 All other trademarks and copyrights are the property of their respective owners. (function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){ {/eq} units to the left, if {eq}C>0 {/eq}. {/eq}, the period of the cosine function is {eq}\dfrac{2\pi}{|B|} As we can see, the cosine function and its period can show up very easily in the world around us, so it's a good idea to tuck this newly acquired knowledge into our mathematical toolboxes to be used when we need it. {/eq} stretched the graph vertically. Find the limit. {/eq}. A good grasp of the number line is also crucial for building a strong number sense. Anyone can earn imaginable degree, area of CALCULUS, JMAP RESOURCE ARCHIVES {/eq} differ from the graph of {eq}f(x)
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