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Name: Christine
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I tutor a 10th grade student in honors algebra 2 and he has been asked to find real world equations involving conic sections in non-standard form. The purpose of this is for him to be able to rewrite the equations in standard form and find all related info (foci, vertex, etc) from the equations while at the same time seeing that math is used in the world around us. Please send any equations and tell where they are used.


One such example is a rolling wave on the ocean surfaces. The water doesn't travel with the waves. The water moves both up-and-down and back-and-forth. The vertical motion, as a function of time, is sinusoidal: y=(y_0)*sin(w*t). The horizontal motion is also sinusoidal, but out of phase with the vertical motion: x=(x_0)*cos(w*t). x_0 and y_0 are constants, the horizontal and vertical amplitudes. w is the angular frequency, a constant often measured in radians per second. t is time, a variable representing the passage of time. As time passes, the water often moves in an elliptical pattern when viewed from the side. If the amplitudes are equal, the pattern is circular.

Dr. Ken Mellendorf
Physics Instructor
Illinois Central College

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