# Tagged Questions

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

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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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### 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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### 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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### 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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### Calculating the angle between the line joining two points and the x-axis [closed]

I need to calculate the angle between two points, the returned result should between $0$ to $2π$ and getAngle[point1, point2]==getAngle[point2, point1]. I have ...
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### What does mean |sin(z)|<=1? [closed]

I already know that the magnitude of sin(z) its equal to sqrt(sin^2(x)+sinh^2(y))
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### Maximizing a trigonometric function

This is probably a naive question, but here it goes: I know that $$r\cos a+s\cos b+t\cos c \leq \frac{rs}{2t}+\frac{rt}{2s}+\frac{ts}{2r},$$ subject to the conditions $a+b+c=\pi$ and $r,s,t$ are ...
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### Put a trigonometric equation in the form A*cos(theta)+B*sin(theta)+C=0 [closed]

eq = (Cos[Θ[t]]cf - Cos[γ1[t]] mf + Cos[γ2[t]] mf)^2/cf^2 + (Sin[Θ[t]]cf + Sin[γ1[t]] mf - Sin[γ2[t]] mf + xP1[t] - xP2[t])^2/cf^2 Can you help me to simplify and ...
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### Replacement of a group of variables in trigonometric expression

I would like to make simplification of trigonometric expressions by using a replacement a group of variables. Here the equation I have to simplify : ...
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### Simplifying a trigonometric function with arctan

Why is this trigonometric expression with $\arctan$ not simplified ? ArcTan[Tan[γ[t] - θ[t]]]
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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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### Force Mathematica to simplify an ArcTan[]?

I understand that there are many solutions that will produce the same arctangent, nevertheless I really need a simplification: ...