Graph the curve 𝑥 = sin(𝑡) + sin(1.5𝑡) , 𝑦 = cos(𝑡). Then find the length of the curve correct to four decimal places. Be sure to graph the entire shape.

I tired ParametricPlot[{Sin (t) + Sin (1.5 t), Cos (t)}, {t, -4, 4}] but nothing came out to the graph

I also tried solve[(-sin (t))/(Cos (t) + Cos (1.5 t)*1.5)] but it didnt come out right


closed as off-topic by QuantumDot, JimB, m_goldberg, Artes, garej Sep 15 '17 at 9:04

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  • "This question arises due to a simple mistake such as a trivial syntax error, incorrect capitalization, spelling mistake, or other typographical error and is unlikely to help any future visitors, or else it is easily found in the documentation." – QuantumDot, JimB, m_goldberg, Artes, garej
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  • $\begingroup$ Functions use square brackets [ ] not parentheses ( ), and all commands are case sensitive, so sin is not the same as Sin. $\endgroup$ – bill s Sep 15 '17 at 1:35
  • 1
    $\begingroup$ What is section 10.2 [DASH] #47? Did you just copy-paste a homework problem here? Those are emphatically not welcome. This online book is a great resource for beginners. $\endgroup$ – QuantumDot Sep 15 '17 at 1:44
  • $\begingroup$ Sorry, i wont do it again, but i have another question when i put in Solve[-sin[t]/(Cos[t] + Cos[1.5 t]*1.5)] im supposed to be getting a decimal but im not getting anything, what am i doing wrong $\endgroup$ – myles roddy Sep 15 '17 at 1:50
  • $\begingroup$ capitalize 's' in Sin, and Solve takes an equation. Read the documentation, and follow the examples. $\endgroup$ – QuantumDot Sep 15 '17 at 1:55
  • $\begingroup$ @mylesroddy there is nothing to solve for in your Solve function. Mathematically, it is inconsistent. $\endgroup$ – Rumplestillskin Sep 15 '17 at 5:02

For the "entire shape" you must extend the range of t to a range of 24 Pi/5

x[t_] := Sin[t] + Sin[3/2 t];
y[t_] := Cos[t];

pp = ParametricPlot[{x[t], y[t]}, {t, -12 Pi/5, 12 Pi/5}]

enter image description here

length = NIntegrate[Sqrt[x'[t]^2 + y'[t]^2],
   {t, -12Pi/5, 12Pi/5}]//NumberForm[#, {6, 4}]&

(*  18.4730  *)

Breaking the integral into multiple segments

intervals = Partition[
   SortBy[t /. Solve[{x[t] == 0, -12 Pi/5 <= t <= 12 Pi/5}, t], N],
   2, 1];

Total[NIntegrate[Sqrt[x'[t]^2 + y'[t]^2],
    {t, #[[1]], #[[2]]}] & /@ intervals]

(*  18.473  *)
  • $\begingroup$ would i just press enter after implementing that or should i put in an extra step $\endgroup$ – myles roddy Sep 15 '17 at 3:05
  • $\begingroup$ When i Implement it i get something different from 18.4730 $\endgroup$ – myles roddy Sep 15 '17 at 3:09
  • $\begingroup$ Did you clear previous definitions or else start with a fresh kernel? $\endgroup$ – Bob Hanlon Sep 15 '17 at 3:19
  • $\begingroup$ should i clear Nintegrate? $\endgroup$ – myles roddy Sep 15 '17 at 3:31

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