I'm new to Mathematica and I am struggling with the Syntax and the functions of this "programming" language.

I'm looking for a way to solve sin2 α cos3 α = tan4 α

But if I try to run it through the Solve[] function I recieve an error.

I'm not looking for hand holding and having someone give me the answer. What I am trying to do is to learn which functions work where and how I successfully can calculate questions like these in Mathematica.

  • $\begingroup$ Welcome to Mathematica.SE! I suggest the following: 1) As you receive help, try to give it too, by answering questions in your area of expertise. 2) Take the tour and check the faqs! 3) When you see good questions and answers, vote them up by clicking the gray triangles, because the credibility of the system is based on the reputation gained by users sharing their knowledge. Also, please remember to accept the answer, if any, that solves your problem, by clicking the checkmark sign $\endgroup$
    – Dunlop
    Oct 17, 2020 at 17:43
  • 1
    $\begingroup$ You have to be careful of the syntax. Sin, Cos and Tan all have capital letters to start with, and also use square brackets i.e. Sin[2 alpha], etc... The other thing you have to be careful about is the use of the = sign. For solving equations you use the double == . Check in the help for Solve for examples and it should be fairly clear $\endgroup$
    – Dunlop
    Oct 17, 2020 at 17:45
  • $\begingroup$ One good place to look is the help page for Solve. Help > Wolfram Documentation > Solve will get you there. $\endgroup$ Oct 17, 2020 at 18:06

1 Answer 1


eqn = Sin[2 a] Cos[3 a] == Tan[4 a];

The functions are periodic so there are many periodic solutions.

Solve[eqn, a] // Short[#, 4] &

enter image description here

Restrict the range of a to some region of interest

sol = Solve[{eqn, 0 <= a <= 2 Pi}, a]

enter image description here

The approximate numeric values are

sol // N

(* {{a -> 0.}, {a -> 1.5708}, {a -> 3.14159}, {a -> 4.71239}, {a -> 
   6.28319}, {a -> 5.60235}, {a -> 0.680831}, {a -> 4.11126}, {a -> 2.17193}} *)


Plot[Evaluate[List @@ eqn], {a, 0, 2 Pi},
 Epilog -> {Red, AbsolutePointSize[6], Point[{a, eqn[[1]]} /. sol]}, 
 PlotLegends -> "Expressions"]

enter image description here

  • $\begingroup$ Wow, thank you so very much Bob! This is way beyond what I was expecting. Again, thank you very very much! $\endgroup$ Oct 18, 2020 at 10:52

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