Answered Essay: Parametric Graph is shown below x = sin t + sin 1.5t, y = cos t Consider the equation x = sin t + sin 1.5t, r = cos t Differentiate With respect to 't'

D Chegg Study TEXTBOOK SOLUTIONS EXPERT Q&A Show a Chapter 10.2, Problem 47E Bookmark Step 1 of 3 Parametric Graph is shown below x= sint+5in1 St,y= cost Comment Step 2 1080
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Parametric Graph is shown below x = sin t + sin 1.5t, y = cos t Consider the equation x = sin t + sin 1.5t, r = cos t Differentiate With respect to ‘t’

Expert Answer


For 2 functions to be graphed simpultaneously, we have to use ParametricPlot[{fx,fy},{t,tmin,tmax}]

Here fx is function of x and fy is function of y.

Consider fx=sin1.5t+sint

sin has a periodicty of 2pi So fx will be periodic when sin 1.5t as well as sin t are same as sin 2pi. Or when 1.5t and t are multiples of 2pi. This happens at t=4pi. Hance fx has periodicity of 4pi

Now consider fy=cost. This has periodicity of 2pi.

So conidering periodicty of both fx and fy, the periodicty for the common graph will be 4pi. So lets take tmin as 0 and tmax as 4pi.

Hence we can use the following statement:

ParametricPlot[{sin[t]+ sin[1.5t], cos t},{t,0,4 pi}]


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