# Tagged Questions

Questions on trigonometric and hyperbolic functions, as well as their inverses, in Mathematica.

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### Why do these calculations 'stop'? [duplicate]

Question 1: If I change guess to a integer, for example guess = 1 then ListPlot already stops at $n=50$. This seems strange to me, any ideas on why this happens? ...
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### Simplify a complex trigonometric equation resulting from constraint solving

In the solving of mechanical constraints, I often meet complex trigonometric equation that I have to simplify. Here the equation I would like to simplify : Mathematica notebook presenting the ...
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### Solving equation containing ArcTan terms

IN MY EDIT I DESCRIBE HOW I GOT TO THAT EXPRESSION AND THE ORIGINAL PROBLEM. I have this expression: ...
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### Do not understand the result I'm getting from Solve [closed]

I did Solve[k2 Cos[x] - k1 Sin[x] == 0,x] Since tangent is sin over cos, the solution must be arctan(k2/k1) But ...
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### Rule/Replace/Patterns [closed]

I need help with doing this question. given: Sin[x+y] Cos[x+y+z] Define using Patterns a rule (specifically a list of 2 rules ) , the two adding rules for trigonometric functions sin (a + b )...
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### How do you collect trigonometric functions in a polynomial?

I have an expression that has various forms of Sin and Cos and I want to collect them specifically so that I can make substitutions. As you can see I cannot figure out how to separate i Cos[theta] ...
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### Simplifying ArcTan[Cos[u], Sin[u]]

I am trying to evaluate the following expression in Mathematica: $$\bigg| \frac{\left(1-z^{-2}\right)^n}{\left(1-z^{-1}\right) \left(2-z^{-n}-z^{-1}\right)} \bigg|^2$$ Here $z$ is the complex ...
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### Indefinite integral of nested trig functions [closed]

I tried vainly to integrate nested trig functions like Integrate[Sin[Cos[x]], x] Mathematica does not find a solution. At first I thought there was no solution, ...
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### How can PowerExpand be made to evaluate the ArcTan form that takes two arguments?

Consider c = Cos[phi]; s = Sin[phi]; ArcTan[c, s] // PowerExpand ArcTan[s/c] // PowerExpand which yields ...
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### Simplify $\tan(\arctan(a) - \arctan(b))$

I want to simplify the expression $\tan(\arctan(a) - \arctan(b))$ to $\tfrac{a-b}{1+a\cdot b}$ (if $b \neq - \tfrac{1}{a}$). Right now, the output of ...
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### Tangent of 2 times arc cosine of -3/4 [closed]

Tan[ArcCos[-3/4] Returns the exact answer: -(Sqrt[7]/3) But: Tan[2 ArcCos[-3/4]] Does not return an exact answer. Any way ...
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### Solve simple trig equation

I would like to solve this equation: $$-x\sin(x)=\cos(x)$$ But Solve in Mathematica doesn't work: This system cannot be solved with the methods available to ...