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# PRECALC ALG & TRIG MAC 1147

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This 7 page Class Notes was uploaded by Marquise Graham on Saturday September 19, 2015. The Class Notes belongs to MAC 1147 at University of Florida taught by Larissa Williamson in Fall. Since its upload, it has received 8 views. For similar materials see /class/207048/mac-1147-university-of-florida in Calculus and Pre Calculus at University of Florida.

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Date Created: 09/19/15

L19 Graphing General Sinusoidal Functions Graphs of Other Trigonometric Functions Graphing General Sinusoidal Functions y Asinmx 740 Asi l z ii j8 a gt 0 a y Acosmx 740 ACOSZUX EB a gt 0 a Amplitude Period Phase shift Vertical shift 1 Determine the amplitude A and period T a 2 Find the xcoordinate ofthe starting key point of one cycle 7 phase shift and the ending point 7T a a 3 Divide the period Thy 4 4 Find the xcoordinates ofthe other 3 key points T Tjr rjr T 77 77 7 a 4 a 4 4 4 4 4 5 Find the ycoordinates of the ve key points 6 Plot the ve key points in the coordinate system 7 Fill in one cycle ofthe a h 8 Continue the graph periodically to make it complete Example Graph y 73sin2x jl Example Find the sinusoidal function y Asinmx7 B from the graph given below Note Amplitude Al maximum Value minimum Value 2 Vertical shift 3 W Blood Pressure P 1007 20cos 8 rtj approximates the blood pressure P in mm ofmercury at time t in seconds a Find the period of the function one cycle one heartbeat b Find the number ofheartbeats cycles per minute c Find the maximum and minimum blood pressure The Graph of y tanx The vertical asymptotes and key points of the graph of tan x39 Domain Range Period Symmetry Vertical Asymptotes Interc epts The Graph of y cotx The vertical asymptotes and key points of the graph of y cotx39 Domain Range Period Symmetry Vertical Asymptotes Interc epts Graphing y Atanmx 7 4 and y Acotmx 7 4 1 Find the period of the function T i a 2 Determine the Vertical asymptotes on one period Set It It mx7 73 and mx7 foryAtanmx7 mx7 0 and mx7 r for yAcotmx7 then solve for x 3 Divide the interval between the asymptotes into 4 parts and nd the xcoordinates of the 3 key points 4 Find the ycoordinates of the key points 5 Plot the asymptotes and key points 6 Fill in one cycle ofthe graph 7 Continue the graph periodically to make it complete Example Graph y tang Examgle Graph y 72 cot Ir x 4 j The graph oI y cscx slnx Domain Range Period Symmehy Vertic al A symptotes Intercepts The graph of y secx cos x Domain Range Period Symmetry Vertical Asymptotes Intercepts Example Graph y secx Example Give the equation ofa function that may have the following graph

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